Numerical analysis Books

Book SynopsisThis book presents the first comprehensive account of fast sequential Monte Carlo (SMC) methods for counting and optimization at an exceptionally accessible level. Written by authorities in the field, it places great emphasis on cross-entropy, minimum cross-entropy, splitting, and stochastic enumeration.Table of ContentsPreface xi 1. Introduction to Monte Carlo Methods 1 2. Cross-Entropy Method 6 2.1. Introduction 6 2.2. Estimation of Rare-Event Probabilities 7 2.3. Cross-Entrophy Method for Optimization 18 2.3.1. The Multidimensional 0/1 Knapsack Problem 21 2.3.2. Mastermind Game 23 2.3.3. Markov Decision Process and Reinforcement Learning 25 2.4. Continuous Optimization 31 2.5. Noisy Optimization 33 2.5.1. Stopping Criterion 35 3. Minimum Cross-Entropy Method 37 3.1. Introduction 37 3.2. Classic MinxEnt Method 39 3.3. Rare Events and MinxEnt 43 3.4. Indicator MinxEnt Method 47 3.4.1. Connection between CE and IME 51 3.5. IME Method for Combinatorial Optimization 52 3.5.1. Unconstrained Combinatorial Optimization 52 3.5.2. Constrained Combinatorial Optimization: The Penalty Function Approach 54 4. Splitting Method for Counting and Optimization 56 4.1. Background 56 4.2. Quick Glance at the Splitting Method 58 4.3. Splitting Algorithm with Fixed Levels 64 4.4. Adaptive Splitting Algorithm 68 4.5. Sampling Uniformly on Discrete Regions 74 4.6. Splitting Algorithm for Combinatorial Optimization 75 4.7. Enhanced Splitting Method for Counting 76 4.7.1. Counting with the Direct Estimator 76 4.7.2. Counting with the Capture–Recapture Method 77 4.8. Application of Splitting to Reliability Models 79 4.8.1. Introduction 79 4.8.2. Static Graph Reliability Problem 82 4.8.3. BMC Algorithm for Computing S(Y) 84 4.8.4. Gibbs Sampler 85 4.9. Numerical Results with the Splitting Algorithms 86 4.9.1. Counting 87 4.9.2. Combinatorial Optimization 101 4.9.3. Reliability Models 102 4.10. Appendix: Gibbs Sampler 104 5. Stochastic Enumeration Method 106 5.1. Introduction 106 5.2. OSLA Method and Its Extensions 110 5.2.1. Extension of OSLA: nSLA Method 112 5.2.2. Extension of OSLA for SAW: Multiple Trajectories 115 5.3. SE Method 120 5.3.1. SE Algorithm 120 5.4. Applications of SE 127 5.4.1. Counting the Number of Trajectories in a Network 127 5.4.2. SE for Probabilities Estimation 131 5.4.3. Counting the Number of Perfect Matchings in a Graph 132 5.4.4. Counting SAT 135 5.5. Numerical Results 136 5.5.1. Counting SAW 137 5.5.2. Counting the Number of Trajectories in a Network 137 5.5.3. Counting the Number of Perfect Matchings in a Graph 140 5.5.4. Counting SAT 143 5.5.5. Comparison of SE with Splitting and SampleSearch 146 A. Additional Topics 148 A.1. Combinatorial Problems 148 A.1.1. Counting 149 A.1.2. Combinatorial Optimization 154 A.2. Information 162 A.2.1. Shannon Entropy 162 A.2.2. Kullback–Leibler Cross-Entropy 163 A.3. Efficiency of Estimators 164 A.3.1. Complexity 165 A.3.2. Complexity of Randomized Algorithms 166 Bibliography 169 Abbreviations and Acronyms 177 List of Symbols 178 Index 181

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Book SynopsisAn informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlightedTable of ContentsPreface xv Acknowledgements xix About the Companion Website xxi 1 Introduction 1 1.1 Numerical Modelling 1 1.2 Overview of the Scaled Boundary Finite Element Method 6 1.3 Features and Example Applications of the Scaled Boundary Finite Element Method 10 1.3.1 Linear Elastic Fracture Mechanics: Crack Terminating at Material Interface 11 1.3.2 Automatic Mesh Generation Based on Quadtree/Octree 13 1.3.3 Treatment of Non-matching Meshes 14 1.3.4 Crack Propagation 17 1.3.5 Adaptive Analysis 17 1.3.6 TransientWave Scattering in an Alluvial Basin 19 1.3.7 Automatic Image-based Analysis 19 1.3.7.1 Two-dimensional Elastoplastic Analysis of Cast Iron 20 1.3.7.2 Three-dimensional Concrete Specimen 22 1.3.8 Automatic Analysis of STL Models 24 1.4 Summary 26 Part I Basic Concepts and MATLAB Implementation of the Scaled Boundary Finite Element Method in Two Dimensions 27 2 Basic Formulations of the Scaled Boundary Finite Element Method 31 2.1 Introduction 31 2.2 Modelling of Geometry in Scaled Boundary Coordinates 31 2.2.1 S-domains: Scaling Requirement on Geometry, Scaling Centre and Scaling of Boundary 31 2.2.2 S-elements: Boundary Discretization of S-domains 37 2.2.3 Scaled Boundary Transformation 40 2.2.3.1 Scaled Boundary Coordinates 40 2.2.3.2 Coordinate Transformation of Partial Derivatives 42 2.2.3.3 Geometrical Properties in Scaled Boundary Coordinates 44 2.3 Governing Equations of Linear Elasticity in Scaled Boundary Coordinates 50 2.4 Semi-analytical Representation of Displacement and Strain Fields 51 2.5 Derivation of the Scaled Boundary Finite Element Equation by the Virtual Work Principle 53 2.5.1 Virtual Displacement and Strain Fields in Scaled Boundary Coordinates 54 2.5.2 Nodal Force Functions 54 2.5.3 The Scaled Boundary Finite Element Equation 55 2.6 Computer Program Platypus: Coefficient Matrices of an S-element 63 2.6.1 Element Coefficient Matrices of a 2-node Line Element 63 2.6.2 Assembly of Coefficient Matrices of an S-element 67 3 Solution of the Scaled Boundary Finite Element Equation by Eigenvalue Decomposition 73 3.1 Solution Procedure for the Scaled Boundary Finite Element Equations in Displacement 73 3.2 Pre-conditioning of Eigenvalue Problems 77 3.3 Computer Program Platypus: Solution of the Scaled Boundary Finite Element Equation of a Bounded S-element by the Eigenvalue Method 78 3.4 Assembly of S-elements and Solution of Global System of Equations 84 3.4.1 Assembly of S-elements 84 3.4.2 Surface Tractions 85 3.4.3 Enforcing Displacement Boundary Conditions 87 3.5 Computer Program Platypus: Assembly and Solution 87 3.5.1 Assembly of Global Stiffness Matrix 87 3.5.2 Assembly of Load Vector 95 3.5.3 Solution of Global System of Equations 96 3.5.4 Utility Functions 97 3.6 Examples of Static Analysis Using Platypus 102 3.7 Evaluation of Internal Displacements and Stresses of an S-element 111 3.7.1 Integration Constants and Internal Displacements 111 3.7.2 Strain/Stress Modes and Strain/Stress Fields 112 3.7.3 Shape Functions of Polygon Elements Modelled as S-elements 114 3.8 Computer Program Platypus: Internal Displacements and Strains 114 3.9 Body Loads 132 3.10 Dynamics and Vibration Analysis 135 3.10.1 Mass Matrix and Equation of Motion 135 3.10.2 Natural Frequencies and Mode Shapes 140 3.10.3 Response History Analysis Using the Newmark Method 143 4 Automatic Polygon Mesh Generation for Scaled Boundary Finite Element Analysis 149 4.1 Introduction 149 4.2 Basics of Geometrical Representation by Signed Distance Functions 150 4.3 Computer Program Platypus: Generation of Polygon S-elementMesh 154 4.3.1 Mesh Data Structure 157 4.3.2 Centroid of a Polygon 165 4.3.3 Converting a TriangularMesh to an S-elementMesh 166 4.3.4 Use of Polygon Meshes Generated by PolyMesher in a Scaled Boundary Finite Element Analysis 171 4.3.5 Dividing Edges of Polygons into Multiple Elements 172 4.4 Examples of Scaled Boundary Finite Element Analysis Using Platypus 175 4.4.1 A Deep Beam 178 4.4.1.1 Static Analysis 186 4.4.1.2 Modal Analysis 189 4.4.1.3 Response History Analysis 190 4.4.1.4 Pure Bending of a Beam: 2 Line Elements on an Edge of Polygons 190 4.4.2 A Circular Hole in an Infinite Plane Under Remote Uniaxial Tension 193 4.4.3 An L-shaped Panel 197 4.4.3.1 Static Analysis 203 4.4.3.2 Modal Analysis 204 4.4.3.3 Response History Analysis 207 5 Modelling Considerations in the Scaled Boundary Finite Element Analysis 209 5.1 Effect of Location of Scaling Centre on Accuracy 209 5.2 Mesh Transition 212 5.2.1 Local Mesh Refinement 212 5.2.2 Rapid Mesh Transition 214 5.2.3 Effect of Nonuniformity of Line Element Length on the Boundary of S-elements 216 5.3 Connecting Non-matching Meshes of Multiple Domains 218 5.3.1 Computer Program Platypus: Combining Two Non-matching Meshes 220 5.3.2 Computer Program Platypus: Modelling of a Problem by Multiple Domains with Non-matching Meshes 223 5.3.3 Examples 225 5.4 Modelling of Stress Singularities 234 Part II Theory and Applications of the Scaled Boundary Finite Element Method 237 6 Derivation of the Scaled Boundary Finite Element Equation in Three Dimensions 239 6.1 Introduction 239 6.2 Scaling of Boundary 239 6.3 Boundary Discretization of an S-domain 242 6.3.1 Isoparametric Quadrilateral Elements 243 6.3.1.1 Four-node Quadrilateral Element 243 6.3.1.2 Quadrilateral Element of Variable Number of Nodes 245 6.3.2 Isoparametric Triangular Elements 246 6.3.2.1 Three-node Triangular Elements 247 6.3.2.2 Six-node Triangular Elements 248 6.4 Scaled Boundary Transformation of Geometry 249 6.5 Geometrical Properties in Scaled Boundary Coordinates 253 6.6 Governing Equations of Elastodynamics with Geometry in Scaled Boundary Coordinates 257 6.7 Derivation of the Scaled Boundary Finite Element Equation by the Galerkin’s Weighted Residual Technique 259 6.7.1 Displacement, Strain Fields and Nodal Force Functions in Scaled Boundary Coordinates 259 6.7.2 The Scaled Boundary Finite Element Equation 262 6.8 Unified Formulations in Two andThree Dimensions 267 6.9 Formulation of the Scaled Boundary Finite Element Equation as a System of First-order Differential Equations 268 6.10 Properties of Coefficient Matrices 269 6.10.1 Coefficient Matrices [E0] and [M0] 270 6.10.2 Coefficient Matrix [E2] 270 6.10.3 Matrix [Zp] 271 6.11 Linear Completeness of the Scaled Boundary Finite Element Solution 272 6.11.1 Constant Displacement Field 272 6.11.2 Linear Displacement Field 273 6.12 Scaled Boundary Finite Element Equation in Stiffness 278 7 Solution of the Scaled Boundary Finite Element Equation in Statics by Schur Decomposition 281 7.1 Introduction 281 7.2 Basics of Matrix Exponential Function 283 7.3 Schur Decomposition 287 7.3.1 Introduction 287 7.3.2 Treatment of the Diagonal Block of Eigenvalues of 0 288 7.4 Solution Procedure for a Bounded S-element by Schur Decomposition 291 7.4.1 Transformation of the Scaled Boundary Finite Element Equation 291 7.4.2 Enforcing the Boundary Condition at the Scaling Centre 292 7.4.3 Determining the Solution for Displacement and Nodal Force Functions 294 7.4.4 Determining the Static Stiffness Matrix 295 7.5 Solution of Displacement and Stress Fields of an S-element 295 7.5.1 Integration Constants 295 7.5.2 Stress Modes and Stresses on the Boundary 296 7.6 Block-diagonal Schur Decomposition 297 7.7 Solution Procedure by Block-diagonal Schur Decomposition 303 7.7.1 General Solution of the Scaled Boundary Finite Element Equation 303 7.7.1.1 [Zp] Having No Eigenvalues of Zero 304 7.7.1.2 [Zp] Having Eigenvalues of Zero 304 7.7.2 Solution for Bounded S-elements 305 7.7.3 Solution for Unbounded S-elements 307 7.7.3.1 [Zp] Having No Eigenvalues of Zero 307 7.7.3.2 [Zp] Having Eigenvalues of Zero 308 7.8 Displacements and Stresses of an S-element by Block-diagonal Schur Decomposition 310 7.8.1 Integration Constants and Displacement Fields 310 7.8.2 Stress Modes and Stress Fields 311 7.8.3 Shape Functions of Polytope Elements 312 7.9 Body Loads 313 7.10 Mass Matrix 315 7.11 Remarks 317 7.12 Examples 319 7.12.1 Circular Cavity in Full-plane 319 7.12.2 Bi-materialWedge 322 7.12.3 Interface Crack in Anisotropic Bi-material Full-plane 325 7.13 Summary 327 8 High-order Elements 329 8.1 Lagrange Interpolation 330 8.2 One-dimensional Spectral Elements 333 8.2.1 Shape Functions 334 8.2.2 Numerical Integration of Element Coefficient Matrices 337 8.2.2.1 Gauss-Legendre Quadrature 337 8.2.2.2 Gauss-Lobatto-Legendre Quadrature 338 8.3 Two-dimensional Quadrilateral Spectral Elements 341 8.3.1 Shape Functions 341 8.3.2 Integration of Element Coefficient Matrices by Gauss-Lobatto-Legendre Quadrature 342 8.4 Examples 344 8.4.1 A Cantilever Beam Subject to End Loading 345 8.4.2 A Circular Hole in an Infinite Plate 347 8.4.3 An L-shaped Panel 349 8.4.4 A 3D Cantilever Beam Subject to End-shear Loading 351 8.4.5 A Pressurized Hollow Sphere 352 9 Quadtree/Octree Algorithm of Mesh Generation for Scaled Boundary Finite Element Analysis 355 9.1 Introduction 355 9.1.1 Mesh Generation 355 9.1.2 The Quadtree/Octree Algorithm 357 9.2 Data Structure of S-element Meshes 360 9.3 Quadtree/Octree Mesh Generation of Digital Images 361 9.3.1 Illustration of Quadtree Decomposition of Two-dimensional Images by an Example 361 9.3.2 Octree Decomposition 366 9.4 Solutions of S-elements with the Same Pattern of Node Configuration 370 9.4.1 Two-dimensional S-elements 370 9.4.2 Three-dimensional S-elements 372 9.5 Examples of Image-based Analysis 374 9.5.1 A 2D Concrete Specimen 374 9.5.2 A 3D Concrete Specimen 376 9.6 Quadtree/Octree Mesh Generation for CAD Models 378 9.6.1 Quadtree/Octree Grid 380 9.6.2 Trimming of Boundary Cells 381 9.7 Examples Using Quadtree/Octree Meshes of CAD Models 383 9.7.1 Square Body with Multiple Holes 384 9.7.2 An Evolving Void in a Square Body 385 9.7.3 Adaptive Analysis of an L-shaped Panel 386 9.7.4 A Mechanical Part 387 9.7.5 STL Models 389 9.8 Remarks 394 10 Linear Elastic Fracture Mechanics 395 10.1 Introduction 395 10.2 Basics of Fracture Analysis: Asymptotic Solutions, Stress Intensity Factors, and the T-stress 397 10.2.1 Crack in Homogeneous Isotropic Material 397 10.2.2 Interfacial Cracks between Two Isotropic Materials 401 10.2.3 Interfacial Cracks between Two AnisotropicMaterials 402 10.2.4 Multi-materialWedges 405 10.3 Modelling of Singular Stress Fields by the Scaled Boundary Finite Element Method 406 10.4 Stress Intensity Factors and the T-stress of a Cracked Homogeneous Body 407 10.5 Definition and Evaluation of Generalized Stress Intensity Factors 416 10.6 Examples of Highly Accurate Stress Intensity Factors and T-stress 432 10.6.1 A Single Edge-cracked Rectangular Body Under Tension 433 10.6.2 A Single Edge-cracked Rectangular Body Under Bending 435 10.6.3 A Centre-cracked Rectangular Body Under Tension 437 10.6.4 A Double Edge-cracked Rectangular Body Under Tension 438 10.6.5 A Single Edge-cracked Rectangular Body Under End Shearing 439 10.7 Modelling of Crack Propagation 440 10.7.1 Modelling of Crack Paths by Polygon Meshes 442 10.7.2 Modelling of Crack Paths by Quadtree Meshes 443 10.7.3 Examples of Crack PropagationModelling 444 10.7.3.1 Fatigue Crack Propagation Using Polygon Mesh 444 10.7.3.2 Crack Propagation in a Beam with Three Holes 447 Appendix A Governing Equations of Linear Elasticity 449 A.1 Three-dimensional Problems 449 A.1.1 Strain 449 A.1.2 Stress and Equilibrium Equation 450 A.1.3 Stress-strain Relationship and Material Elasticity Matrix 451 A.1.4 Boundary Conditions 453 A.2 Two-dimensional Problems 454 A.2.1 Elasticity Matrix in Plane Stress 455 A.2.2 Elasticity Matrix in Plane Strain 456 A.3 Unified Expressions of Governing Equations 457 Appendix B Matrix Power Function 459 B.1 Definition of Matrix Power Function 459 B.2 Application to Solution of System of Ordinary Differential Equations 460 B.3 Computation of Matrix Power Function by Eigenvalue Method 461 Bibliography 463 Index 475

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Book SynopsisApproaches computational engineering sciences from the perspective of engineering applications Uniting theory with hands-on computer practice, this book gives readers a firm appreciation of the error mechanisms and control that underlie discrete approximation implementations in the engineering sciences. Key features: Illustrative examples include heat conduction, structural mechanics, mechanical vibrations, heat transfer with convection and radiation, fluid mechanics and heat and mass transport Takes a cross-discipline continuum mechanics viewpoint Includes Matlab toolbox and .m data files on a companion website, immediately enabling hands-on computing in all covered disciplines Website also features eight topical lectures from the author's own academic courses It provides a holistic view of the topic from covering the different engineering problems that can be solved using finite element to how each pTable of ContentsPreface viii Notation xi 1 COMPUTATIONAL ENGINEERING SCIENCE 1 1.1 Engineering simulation 1 1.2 A problem solving environment 2 1.3 Problem statements in engineering 4 1.4 Decisions on forming WSN 6 1.5 Discrete approximate WSh implementation 8 1.6 Chapter summary 9 1.7 Chapter references 10 2 PROBLEM STATEMENTS 11 2.1 Engineering simulation 11 2.2 Continuum mechanics viewpoint 12 2.3 Continuum conservation law forms 12 2.4 Constitutive closure for conservation law PDEs 14 2.5 Engineering science continuum mechanics 18 2.6 Chapter references 20 3 SOME INTRODUCTORY MATERIAL 21 3.1 Introduction 21 3.2 Multi-dimensional PDEs, separation of variables 22 3.3 Theoretical foundations, GWSh 27 3.4 A legacy FD construction 28 3.5 An FD approximate solution 30 3.6 Lagrange interpolation polynomials 31 3.7 Chapter summary 32 3.8 Exercises 34 3.9 Chapter references 34 4 HEAT CONDUCTION35 4.1 A steady heat conduction example 35 4.2 Weak form approximation, error minimization 37 4.3 GWSN discrete implementation, FE basis38 4.4 Finite element matrix statement 41 4.5 Assembly of {WS}e to form algebraic GWSh 43 4.6 Solution accuracy, error distribution 45 4.7 Convergence, boundary heat flux 47 4.8 Chapter summary 47 4.9 Exercises 48 4.10 Chapter reference 48 5 STEADY HEAT TRANSFER, n =149 5.1 Introduction 49 5.2 Steady heat transfer, n = 1 50 5.3 FE k = 1 trial space basis matrix library 52 5.4 Object-oriented GWSh programming 55 5.5 Higher completeness degree trial space bases58 5.6 Global theory, asymptotic error estimate 62 5.7 Non-smooth data, theory generalization 66 5.8 Temperature dependent conductivity, non-linearity 69 5.9 Static condensation, p-elements 72 5.10 Chapter summary 75 5.11 Exercises 76 5.12 Computer labs 77 5.13 Chapter references 78 6 ENGINEERING SCIENCES, n =1 79 6.1 Introduction 79 6.2 The Euler-Bernoulli beam equation 80 6.3 Euler-Bernoulli beam theory GWSh reformulation 85 6.4 The Timoshenko beam theory 92 6.5 Mechanical vibrations of a beam 99 6.6 Fluid mechanics, potential flow 106 6.7 Electromagnetic plane wave propagation110 6.8 Convective-radiative finned cylinder heat transfer 112 6.9 Chapter summary 120 6.10 Exercises122 6.10 Computer labs 123 6.11 Chapter references 124 7 STEADY HEAT TRANSFER, n > 1 125 7.1 Introduction 125 7.2 Multi-dimensional FE bases and DOF 126 7.3 Multi-dimensional FE operations 129 7.4 The NC k = 1,2 basis FE matrix library 132 7.5 NC basis {WS}e template, accuracy, convergence 136 7.6 The tensor product basis element family 139 7.7 Gauss numerical quadrature, k = 1 TP basis library 141 7.8 Convection-radiation BC GWSh implementation 146 7.9 Linear basis GWSh template unification 150 7.10 Accuracy, convergence revisited 152 7.11 Chapter summary 153 7.12 Exercises155 7.13 Computer labs 155 7.14 Chapter references 156 8 FINITE DIFFERENCES OF OPINION 159 8.1 The FD-FE correlation159 8.2 The FV-FE correlation162 8.3 Chapter summary 167 8.4 Exercises168 9 CONVECTION-DIFFUSION, n = 1 169 9.1 Introduction169 9.2 The Galerkin weak statement 170 9.3 GWSh completion for time dependence172 9.4 GWSh + qTS algorithm templates 173 9.5 GWSh + qTS algorithm asymptotic error estimates 175 9.6 Performance verification test cases 177 9.7 Dispersive error characterization 180 9.8 A modified Galerkin weak statement 184 9.9 Verification problem statements revisited 187 9.10 Unsteady heat conduction 190 9.11 Chapter summary 193 9.12 Exercises 193 9.13 Computer labs 194 9.14 Chapter references 195 10 CONVECTION-DIFFUSION, n > 1 197 10.1 The problem statement 197 10.2 GWSh + qTS formulation reprise 198 10.3 Matrix library additions, templates 200 10.4 mPDE Galerkin weak forms, theoretical analyses 202 10.5 Verification, benchmarking and validation 207 10.6 Mass transport, the rotating cone verification 208 10.7 The gaussian plume benchmark 211 10.8 The steady n-D Peclet problem verification 213 10.9 Mass transport, a validated n = 3 experiment 215 10.10 Numerical linear algebra, matrix iteration 222 10.11 Newton and AF TP jacobian templates 227 10.12 Chapter summary 229 10.13 Exercises231 10.14 Computer labs 231 10.15 Chapter references232 11 ENGINEERING SCIENCES, n > 1 235 11.1 Introduction 235 11.2 Structural mechanics236 11.3 Structural mechanics, virtual work FE form 240 11.4 Plane stress/strain, GWSh implementation 242 11.5 Elasticity computer lab 246 11.6 Fluid mechanics, incompressible-thermal flow 251 11.7 Vorticity-streamfunction GWSh + qTS algorithm 254 11.8 An isothermal INS validation experiment 258 11.9 Multi-mode convection heat transfer262 11.10 Mechanical vibrations, normal mode GWSh 267 11.11 Normal modes of a vibrating membrane270 11.12 Multi-physics solid-fluid mass transport 276 11.13 Chapter summary 280 11.14 Exercises 282 11.15 Computer labs283 11.14 Chapter references 284 12 CONCLUSION 287 Index 289

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Book SynopsisBasic R Programming.- Random Variable Generation.- Monte Carlo Integration.- Controlling and Accelerating Convergence.- Monte Carlo Optimization.- Metropolis#x2013;Hastings Algorithms.- Gibbs Samplers.- Convergence Monitoring and Adaptation for MCMC Algorithms.Trade ReviewFrom the reviews:“Robert and Casella’s new book uses the programming language R, a favorite amongst (Bayesian) statisticians to introduce in eight chapters both basic and advanced Monte Carlo techniques … . The book could be used as the basic textbook for a semester long course on computational statistics with emphasis on Monte Carlo tools … . useful for (and should be next to the computer of) a large body of hands on graduate students, researchers, instructors and practitioners … .” (Hedibert Freitas Lopes, Journal of the American Statistical Association, Vol. 106 (493), March, 2011)“Chapters focuses on MCMC methods the Metropolis–Hastings algorithm, Gibbs sampling, and monitoring and adaptation for MCMC algorithms. … There are exercises within and at the end of all chapters … . Overall, the level of the book makes it suitable for graduate students and researchers. Others who wish to implement Monte Carlo methods, particularly MCMC methods for Bayesian analysis will also find it useful.” (David Scott, International Statistical Review, Vol. 78 (3), 2010)“The primary audience is graduate students in statistics, biostatistics, engineering, etc. who need to know how to utilize Monte Carlo simulation methods to analyze their experiments and/or datasets. … this text does an effective job of including a selection of Monte Carlo methods and their application to a broad array of simulation problems. … Anyone who is an avid R user and has need to integrate and/or optimize complex functions will find this text to be a necessary addition to his or her personal library.” (Dean V. Neubauer, Technometrics, Vol. 53 (2), May, 2011)Table of ContentsBasic R Programming.- Random Variable Generation.- Monte Carlo Integration.- Controlling and Accelerating Convergence.- Monte Carlo Optimization.- Metropolis#x2013;Hastings Algorithms.- Gibbs Samplers.- Convergence Monitoring and Adaptation for MCMC Algorithms.

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Book SynopsisAs well as providing an overview of the current state of science in the analysis and synthesis of non-rigid shapes, the authors include everyday examples to explain concepts. Practice problems follow at the end of each chapter, along with detailed solutions.Trade ReviewFrom the reviews: "This book provides an introduction to this geometry. … Overall, the book … does explain relevant mathematical notions, such as Gromov’s metric geometry ideas, in a very understandable and entertaining way, with numerous images and exercises. … I highly recommend it to both computer scientists interested in learning more about the latest advances in computational geometry and to geometers looking for applications. This unique book can serve as an excellent textbook for many related courses, for self-study, or as a reference." (V. Kreinovich, ACM Computing Reviews, May, 2009) “Numerical geometry of non-rigid shapes by A. Bronstein, M. Bronstein, and R. Kimmel combines the beauty of modern mathematics … with the interesting field of computer vision and pattern recognition. … The book is developed at an intermediate-advanced level. Students will find the material clear and easy to understand, and will benefit from its good presentation.” (Stefan Henn, Mathematical Reviews, Issue 2010 b)Table of ContentsA Taste of Geometry.- Discrete Geometry.- Shortest Paths and Fast Marching Methods.- Numerical Optimization.- In the Rigid Kingdom.- Multidimensional Scaling.- Spectral Embedding.- Non Euclidean Embedding.- Isometry Invariant Similarity.- Partial Similarity.- Non rigid Correspondence and Calculus of Shapes.- Three dimensional Face Recognition.- Epilogue.

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Book SynopsisHistory of Experimental Structural Mechanics.- Sensors .- Instrumentation.- Applied Digital Signal Processing.- Basic Measurements.- Structural Measurements.- Environmental Measurements.- Design of Tests.- Modal Parameter Estimation.- Modal Analysis of Rotating Systems.- Operating Modal Analysis.- Computational Methods in Structural Dynamics.- Finite/Boundary Element Modeling and Model Reduction.- FE Model Correlation.- Model Updating.- Damping of Materials and Stuctures.- Model Validation/Verification/Calibration.- Uncertainty Quantification and Statistical Issues.- Nonlinear System Analysis.- Rotating System Analysis.- Structural Health Monitoring and Damage Detection.- System Modeling.- Modal Modeling.- Impedance Modeling.- Acoustics of Structural Systems-VibroAcoustics.- Automotive Structural Testing.- Civil Structural Testing.- Aerospace Structural Testing.- Sports Equipment Testing.Table of ContentsHistory of Experimental Structural Mechanics.- Sensors .- Instrumentation.- Applied Digital Signal Processing.- Basic Measurements.- Structural Measurements.- Environmental Measurements.- Design of Tests.- Modal Parameter Estimation.- Modal Analysis of Rotating Systems.- Operating Modal Analysis.- Computational Methods in Structural Dynamics.- Finite/Boundary Element Modeling and Model Reduction.- FE Model Correlation.- Model Updating.- Damping of Materials and Stuctures.- Model Validation/Verification/Calibration.- Uncertainty Quantification and Statistical Issues.- Nonlinear System Analysis.- Rotating System Analysis.- Structural Health Monitoring and Damage Detection.- System Modeling.- Modal Modeling.- Impedance Modeling.- Acoustics of Structural Systems-VibroAcoustics.- Automotive Structural Testing.- Civil Structural Testing.- Aerospace Structural Testing.- Sports Equipment Testing.

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Book SynopsisProceedings volume contains carefully selected papers presented during the 17th IFIP Conference on System Modelling and Optimization.Table of Contents1 On the convergence of a trust region SQP algorithm for nonlinearly constrained optimization problems.- 2 Decomposition and suboptimal control in dynamical systems.- 3 Network flow — theory and applications with practical impact.- 4 The mathematical theory of evidence — a short introduction.- 5 Algebraic methods in control, theory and applications.- 6 One method for robust control of uncertain systems — theory and practice.- 7 Stochastic optimization methods in engineering.- 8 Robust stabilization of nonlinear systems by optimal controllers.- 9 Weighted H2 approximation of transfer functions.- 10 On design of H? optimal controls for uncertain nonlinear systems.- 11 Constrained optimization algorithms and automatic differentiation for parameter estimation with application to granulocytics models.- 12 Expert system for diagnosis of womens’ menstrual cycle using natural family planning method.- 13 Metabolic flux determination by 13-C tracer experiments: analysis of sensitivity, identifiability and redundancy.- 14 Binding-time analysis applied to mathematical algorithms.- 15 Invariant state progress and relation modelling of DEDS.- 16 Remarks on the observability of nonlinear discrete time systems.- 17 Risk-sensitive control and dynamic games: the discrete-time case.- 18 Dynamic portfolio optimization based on reference trajectories.- 19 Stability analysis of time-varying discrete interval systems.- 20 The relaxation theory applied to optimal control problems of semilinear elliptic equations.- 21 On the use of space invariant imbedding to solve optimal control problems for second order elliptic equations.- 22 Semismoothness in parametrized quasi-variational inequalities.- 23 Optimal control problem governed by a semilinear parabolic equation.- 24 Shape optimization of hyperelastic rod.- 25 Dynamic modelling and optimal hierarchical control of a multiple-effect evaporator — superconcentrator plant.- 26 On the use of consistent approximations for the optimal design of beams.- 27 A game-theoretical model for a controlled process of heat transfer.- 28 Constrained predictive control of a counter-current extractor.- 29 Optimal policies under different assumptions about target values: an optimal control analysis for Austria.- 30 Optimal usage of saline and non saline irrigation water; a policy tool.- 31 Fuzzy integer sharing problem with fuzzy capacity constraints.- 32 A fuzzy-PID-concept with minimal rule set.- 33 A numerical procedure for minimizing the maximum cost.- 34 Game of pursuit with zero stop probability.- 35 Solution concepts in multicriteria cooperative games without side payments.- 36 Computer models for maximising tumor cell kill and for minimizing side effects in radiation therapy.- 37 Decision makin& problems: AIDS prevention and energy development.- 38 A mathematical model of HIV infection: the role of CD8+ lymphocytes.- 39 Mathematical modelling of conjugate formation by cytotoxic lymphocytes and tumour cells.- 40 Reliability optimization of complex systems using sharp lower bounds.- 41 Knowledge retrieval for autonomous agents.- 42 Simulation and optimization of complex systems reliability characteristics in grouped data structure.- 43 A modular system of software tools for multicriteria model analysis.- 44 Methodology and modular tool for aspiration-led analysis of LP models.- 45 Interactive multiobjective optimization system NIMBUS applied to nonsmooth structural design problems.- 46 Preliminary computational experience with a descent level method for convex nondifferentiable optimization.- 47 Bundle methods applied to the unit-commitment problem.- 48 Nondifferentiable optimization solver: basic theoretical assumptions.- 49 Discrete approximation of nonlinear control problems.- 50 Convergence of Lagrange—Newton method for control-state and pure state constrained optimal control problems.- 51 Descent methods for optimal periodic hereditary control problems.- 52 Aircraft trajectory optimization using nonlinear programming.- 53 Feedback control of state constrained optimal control problems.- 54 Primal-dual interior point method for multicommodity network flows with side constraints and comparison with alternative methods.- 55 Dual Bregman proximal methods for large-scale 0–1 problems.- 56 On long-step surrogate projection methods for solving convex feasibility problems.- 57 Theoretical and experimental analyis of random linkage algorithms for global optimization.- 58 A dynamic list heuristic for 2D-cutting.- 59 About solving linear integer programs through hermite normal form decomposition.- 60 Software system for solving multi-scale optimization problems.- 61 Dual barrier-projection and barrier-Newton methods in linear programming.- 62 Flow and release optimization in manufacturing systems represented as timed event graphs.- 63 A control model for assembly manufacturing systems.- 64 Numerical experiment on the 2D cutting-stock algorithms based on local optimization.- 65 An algorithm for the transportation problem with given frequencies.- 66 The traveling salesman problem with precedence constraints and binary costs.- 67 Cost oriented competing processes — a new handling of assignment problems.- 68 Modelling and solving of the allocation problem of non-convex polygons with rotations.- 69 Parameters identification of a time-varying stochastic dynamic systems using Viterbi algorithm.- 70 Management of bond portfolios via stochastic programming — postoptimality and sensitivity analysis.- 71 A note on objective functions in multistage stochastic nonlinear programming problems.- 72 Dynamic search for shortest multimodal paths in a transportation network.- 73 Arc routing for rural Irish networks.- 74 Arc routing vehicle routing problems with vehicle/site dependencies.- Index of contributors.- Keyword index.

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Book SynopsisEmploy essential tools and functions of the MATLAB and Simulink packages, which are explained and demonstrated via interactive examples and case studies. This revised edition covers features from the latest MATLAB 2022b release, as well as other features that have been released since the first edition published.  This book contains dozens of simulation models and solved problems via m-files/scripts and Simulink models which will help you to learn programming and modelling essentials. You''ll become efficient with many of the built-in tools and functions of MATLAB/Simulink while solving engineering and scientific computing problems. Beginning MATLAB and Simulink, Second Edition explains various practical issues of programming and modelling in parallel by comparing MATLAB and Simulink. After studying and using this book, you''ll be proficient at using MATLAB and Simulink and applying the source code and models from the book''s examples as templTable of Contents1. Introduction to MATLAB.- 2. Programming Essentials.- 3. Graphical User Interface Model Development.- 4. MEX files, C/C++ and Standalone Applications.- 5. Simulink Modeling Essentials.- 6. Plots.- 7. Matrix Algebra.- 8. Ordinary Differential Equations.

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Book SynopsisPreliminary concepts.- Nonlinear Finite Element Analysis Procedure.- Finite Element Analysis for Nonlinear Elastic Systems.- Finite Element Analysis for Elastoplastic Problems.- Finite Element Analysis for Contact Problems. Table of ContentsPreliminary concepts.- Nonlinear Finite Element Analysis Procedure.- Finite Element Analysis for Nonlinear Elastic Systems.- Finite Element Analysis for Elastoplastic Problems.- Finite Element Analysis for Contact Problems.

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Book SynopsisImplicit Functions and Solution MappingsTrade Review“The book represents the state of the art of the modern theory of inverse and implicit functions and provides an important source for studies of numerical methods and applications in this area. It can be warmly recommended to all specialists and advanced students working in optimization, analysis, numerical mathematics, and other mathematical fields, as well as to all those who apply variational analysis in engineering, physics, operations research, economics, finance, and more.” (Diethard Klatte, SIAM Review, Vol. 57 (2), June, 2015)“The book commences with a helpful context-setting preface followed by six chapters. Each chapter starts with a useful preamble and concludes with a careful and instructive commentary, while a good set of references, a notation guide and a somewhat brief index complete this study. … I unreservedly recommended this book to all practitioners and graduate students interested in modern optimization theory or control theory or to those just engaged by beautiful analysis cleanly described.” (Jonathan Michael Browein, IEEE Control Systems Magazine, February, 2012).“This book is devoted to the theory of inverse and implicit functions and some of its modifications for solution mappings in variational problems. … The book is targeted to a broad audience of researchers, teachers and graduate students. It can be used as well as a textbook as a reference book on the topic. Undoubtedly, it will be used by mathematicians dealing with functional and numerical analysis, optimization, adjacent branches and also by specialists in mechanics, physics, engineering, economics and so on.” (Peter Zabreiko, Zentralblatt MATH, Vol. 1178, 2010).“The present monograph will be a most welcome and valuable addition. … This book will save much time and effort, both for those doing research in variational analysis and for students learning the field. This important contribution fills a gap in the existing literature.” (Stephen M. Robinson, Mathematical Reviews, Issue 2010).Table of ContentsIntroduction and equation-solving background.- Solution mappings for variational problems.- Set-valued analysis of solution mappings.- Regularity properties through generalized derivatives.- Metric regularity in infinite dimensions.- Applications in numerical variational analysis.

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Book SynopsisRandom Number Generators, Principles and Practices has been written for programmers, hardware engineers, and sophisticated hobbyists interested in understanding random numbers generators and gaining the tools necessary to work with random number generators with confidence and knowledge. Using an approach that employs clear diagrams and running code examples rather than excessive mathematics, random number related topics such as entropy estimation, entropy extraction, entropy sources, PRNGs, randomness testing, distribution generation, and many others are exposed and demystified. If you have ever Wondered how to test if data is really random Needed to measure the randomness of data in real time as it is generated Wondered how to get randomness into your programs Wondered whether or not a random number generator is trustworthy Wanted to be able to choose between random number generator solutions Needed to turn uniform random data into a different distribution NeededTable of Contents1 Introduction 1.1 Tools 1.2 Terminology 1.3 The Many Types of Random Numbers 1.3.1 Uniform Random Numbers 2 Random Number Generators 2.1 Classes of Random Number Generators 2.2 Names for RNGs 3 Making Random Numbers 3.1 A Quick Overview of the RNG Types 3.2 The Structure of Full RNG Implementations 3.3 Pool Extractor Structures 3.4 Multiple Input Extractors 4 Physically Uncloneable Functions 21 4.1 The other kind âAS Static vs. Dynamic Random Number Generators . 5 Testing Random Numbers 5.1 Known Answer Tests 5.2 Distinguishing From Random 5.3 PRNG Test Suites 5.4 Entropy Measurements 5.5 Min Entropy Estimation 5.6 Model Equivalence Testing 5.7 Statistical Prerequisite Testing 5.8 The problem Distinguishing Entropy and Pseudo-randomness 5.9 PRNG Tests: DieHarder, NIST SP800-22,TestU01, China ICS 35.040 5.10 Entropy Measurements 5.11 Min Entropy Measurements 5.12 Modeling to Test a Source 5.13 Statistical Prerequisites 5.14 Testing for bias . 5.15 results that are âAŸtoo goodâAZ (E.G. Chi-square == 0.5) 5.16 Distinguishing Correlation from Bias 5.17 Testing for Stationary properties 5.18 FFT analysis 5.19 Online Testing 5.20 Working From the Source RNG 5.21 Tools 5.22 Summary 6 Entropy Extraction or Distillation 6.1 A simple extractor, the XOR gate 6.2 A simple way of improving the distribution of random numbers that have known missing values using XOR 7 Quantifying Entropy 7.1 Rényi Entropy 7.2 Distance From Uniform Topics to put somewhere in the book- in existing chapters and new chapters 8.1 XOR as a 2 bit extractor 8.2 Properties of real random numbers 8.3 Binomial distributions 8.4 Normal distributions 8.4.1 Dice, more dice 8.4.2 Central limit theorem 8.5 Seeing patterns 8.6 Regression to the mean 8.7 Lack of correlation, bias, algorithmic connections, predictability 8.8 What’s a True random number? 8.9 Random numbers in cryptography 8.10 Things they help with liveness, unpredictability, resistance to attacks 8.11 Examples of use 8.11.1 Salting Passwords . 8.11.2 802.11i exchange 8.11.3 PKMv2 exchange 8.11.4 Making Keys 8.12 Examples of RNG crypto failures 8.12.1 Sony PS3 attack 8.12.2 MiFare Classic 8.12.3 Online Poker 8.12.4 Debian OpenSSL Fiasco 8.12.5 Linux Boot Time Entropy 8.13 Humans and random numbers 8.14 Result of asking people for a random number 8.14.1 Normal People 8.14.2 Crypto People 8.15 Mental Random Number Tricks 8.15.1 How to think of a really random number 8.16 PRNGs 8.17 extractors 8.17.1 CBC MAC 8.17.2 BIW 8.17.3 Von Neumann 8.18 Extractor Theory 8.19 Random Number Standards 8.19.1 SP800-90A B C . 8.19.2 Ansi X9.82 8.20 PRNG Algorithms 8.20.1 SP800-90A CTR DRBG 8.20.2 SP800-90A SHA DRBG 8.20.3 XOR Construction 8.20.4 Oversampling Construction 8.21 Yarrow 8.22 Whirlpool 8.23 Linux Kernel random service 8.24 Appendices 8.25 Resources 8.25.1 SW Sources 8.25.2 Online random number sources 8.26 Example Algorithm Vectors 8.26.1 SP800-90A CTR DRBG 128 & 256 8.26.2 SP800-90A Hash DRBG SHA-1 & SHA 256 8.26.3 AES-CBC-MAC Conditioner 128 8.26.4 AES-CBC-MAC Conditioner 8.27 SP800-90 LZ Tests Issues

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Book SynopsisThe recent development of the fuzzy set theory has given scientists the opportunity to model under conditions which are vague or not precisely defined, thus succeeding to solve mathematically problems whose statements are expressed in our natural language. Since Zadeh introduced the concept of fuzzy set in 1965, many efforts have been made by specialists for improving its effectiveness to deal with uncertain, ambiguous and vague situations. As a result a series of extensions and generalizations of the ordinary fuzzy set followed and several theories have been proposed as alternatives to the fuzzy set theory. The spectre of applications of those theories has been rapidly expanded during the last years covering physical sciences, economics and management, expert systems like financial planners, diagnostic, meteorological, information-retrieval, control systems, etc, industry, robotics, decision making, programming, medicine, biology, humanities, education and almost all the other sectors of the human activity, including human reasoning itself. The target of the present book is to become an essential guide to fuzzy sets and systems and to related theories. The whole book consists of ten chapters and a shorter commentary. It starts from the history and an introduction to fuzzy sets and logic and from a brief exposition of related theories. The management of the uncertainty in fuzzy environment as well as the evaluation of fuzzy data, frequently appearing nowadays in science and technology, are also studied. Assessment methods are presented using tools such as triangular fuzzy numbers, fuzzy relation equations and the grey system theory. An introduction to the theory of fuzzy graphs, a review of the hybrids of neural networks and fuzzy logic and an introduction to single valued neutrosophic numbers and the granular calculus of single valued neutrosophic functions are also contained among the topics of the book. More specialized topics include the controllability of non linear fuzzy fractional differential systems, the use of fuzzy probability and fuzzy possibility theory for integrating the voltage sag type detection of electrical networks, the presentation of an algorithm to highlight the importance of using statistical methods in pattern recognition, the study of the known from Physics Goursat problem for a fuzzy hyperbolic equation under the fractional Caputo g-derivative for fuzzy-valued multivariable functions an a hybrid fuzzy potential field method for the navigation of Sumo robots. It is hoped that all the above information can provide a framework to the readers of the book that enable them to proceed to a deeper study of fuzzy systems and the related to them theories.

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Book SynopsisNumerous problems from diverse disciplines can be converted using mathematical modelling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space or Hilbert space or Banach Space or even more general spaces. The solution of these equations is sought in closed form. But this is possible only in special cases. That is why researchers and practitioners use algorithms which seems to be the only alternative. Due to the explosion of technology, scientific and parallel computing, faster and faster computers become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. There is exactly where we come in with our book containing such algorithms with application especially in problems from Economics but also from other areas such as Mathematical: Biology, Chemistry, Physics, Scientific, Parallel Computing, and also Engineering. The book can be used by senior undergraduate students, graduate students, researchers and practitioners in the aforementioned area in the classroom or as a reference material. Readers should know the fundamentals of numerical functional analysis, economic theory, and Newtonian physics. Some knowledge of computers and contemporary programming shall be very helpful to the readers.Table of ContentsPreface; Definition, Existence and Uniqueness of Equilibrium in Oligopoly Markets; Numerical Methodology for Solving Oligopoly Problems; Global Convergence of Iterative Methods with Inverses; Ball Convergence of Third and Fourth Order Methods for Multiple Zeros; Local Convergence of Two Methods for Multiple Roots Eight Order; Choosing the Initial Points for Newtons Method; Extending the Applicability of an Ulm-Like Method under Weak Conditions; Projection Methods for Solving Equations with a Non-differentiable Term; Efficient Seventh Order of Convergence Solver; An Extended Result of Rall-Type for Newtons Method; Extension of Newtons Method for Cone Valued Operators; Inexact Newtons Method under Robinsons Condition; Newtons Method for Generalized Equations with Monotone Operators; Convergence of Newtons method and uniqueness of the solution for Banach Space Valued Equations; Convergence of Newtons method and uniqueness of the solution for Banach Space Valued Equations II; Extended Gauss-Newton Method: Convergence and Uniqueness Results; Newtons Method for Variational Problems: Wangs g-condition and Smales a-theory; Extending the Applicability of Newtons Method; On the Convergence of a Derivative Free Method using Recurrent Functions; Inexact Newton-like Method under Weak Lipschitz Conditions; Ball Convergence Theorem for Inexact Newton Methods in Banach Space; Extending the Semi-Local Convergence of a Stirling-Type Method; Newtons Method for Systems of Equations with Constant Rank Derivatives; Extended Super-Halley Method; Chebyshev-Type Method of Order Three; Extended Semi-Local Convergence of the Chebyshev-Halley Method; Gauss-Newton-Type Schemes for Undetermined Least Squares Problems; Glossary of Symbols.

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Book SynopsisSystems of linear equations are ubiquitous in numerical analysis and scientific computing. and iterative methods are indispensable for the numerical treatment of such systems. This book offers a rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning. The book supplements standard texts on numerical mathematics for first-year graduate and advanced undergraduate courses and is suitable for advanced graduate classes covering numerical linear algebra and Krylov subspace and multigrid iterative methods. It will be useful to researchers interested in numerical linear algebra and engineers who use iterative methods for solving large algebraic systems.Table of ContentsList of figures; List of algorithms; Preface; 1. Krylov subspace methods; 2. Toeplitz matrices and preconditioners; 3. Multigrid preconditioners; 4. Preconditioners by space decomposition; 5. Some applications; Bibliography; Index.

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Book SynopsisInverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data.This book presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles.A Taste of Inverse Problems: Basic Theory and Examples rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations; presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.

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Book Synopsis“If mathematical modeling is the process of turning real phenomena into mathematical abstractions, then numerical computation is largely about the transformation from abstract mathematics to concrete reality. Many science and engineering disciplines have long benefited from the tremendous value of the correspondence between quantitative information and mathematical manipulation.” -from the PrefaceFundamentals of Numerical Computation is an advanced undergraduate-level introduction to the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. The book is organized with simpler methods in the first half and more advanced methods in the second half, allowing use for either a single course or a sequence of two courses. The authors take readers from basic to advanced methods, illustrating them with over 200 self-contained MATLAB functions and examples designed for those with no prior MATLAB experience. Although the text provides many examples, exercises, and illustrations, the aim of the authors is not to provide a cookbook per se, but rather an exploration of the principles of cooking.Professors Driscoll and Braun have developed an online resource that includes well-tested materials related to every chapter. Among these materials are lecture-related slides and videos, ideas for student projects, laboratory exercises, computational examples and scripts, and all the functions presented in the book.

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Book SynopsisIn the intervening years since this book was published in 1981, the field of optimization has been exceptionally lively. This fertility has involved not only progress in theory, but also faster numerical algorithms and extensions into unexpected or previously unknown areas such as semidefinite programming. Despite these changes, many of the important principles and much of the intuition can be found in this Classics version of Practical Optimization.This book provides model algorithms and pseudocode, useful tools for users who prefer to write their own code as well as for those who want to understand externally provided code. It presents algorithms in a step-by-step format, revealing the overall structure of the underlying procedures and thereby allowing a high-level perspective on the fundamental differences. And it contains a wealth of techniques and strategies that are well suited for optimization in the twenty-first century, and particularly in the now-flourishing fields of data science, “big data,” and machine learning. Practical Optimization is appropriate for advanced undergraduates, graduate students, and researchers interested in methods for solving optimization problems.

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Book SynopsisThis textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems—interpolation, integration, linear systems, zero finding, and differential equations—are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises.Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.

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Book SynopsisBased on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area.A Mathematical Introduction to Electronic Structure Theory begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree–Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn–Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy.The book is written for advanced undergraduate and beginning graduate students, specifically those with mathematical backgrounds but without a priori knowledge of quantum mechanics, and can be used for self-study by researchers, instructors, and other scientists. The book can also serve as a starting point to learn about many-body perturbation theory, a topic at the frontier of the study of interacting electrons.

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Book SynopsisDynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks.This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

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Book SynopsisThis companion piece to the author’s 2018 book, A Software Repository for Orthogonal Polynomials, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions.The repository contains 60 datasets, each dealing with a particular weight function. Included are classical, quasi-classical, and, most of all, nonclassical weight functions and associated orthogonal polynomials.

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Book SynopsisNumerical Linear Algebra and Optimization covers the fundamentals of closely related topics: linear systems (linear equations and least-squares) and linear programming (optimizing a linear function subject to linear constraints). For each problem class, stable and efficient numerical algorithms intended for a finite-precision environment are derived and analyzed. In 1991, when the book first appeared, these topics were rarely taught with a unified perspective, and, somewhat surprisingly, this remains true almost 30 years later. As a result, some of the material in this book can be difficult to find elsewhere—in particular, techniques for updating the LU factorization, descriptions of the simplex method applied to all-inequality form, and the analysis of what happens when using an approximate inverse to solve Ax=b.This book is appropriate for students who want to learn about numerical techniques for solving linear systems and/or linear programming using the simplex method.

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Book SynopsisOver seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques.Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com).This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

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Book SynopsisIterative methods use successive approximations to obtain more accurate solutions. Iterative Methods and Preconditioners for Systems of Linear Equations presents historical background, derives complete convergence estimates for all methods, illustrates and provides Matlab codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students in need of an overview or of deeper knowledge about iterative methods. It can be used in courses on Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Scientists and engineers interested in new topics and applications will also find the text useful.

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Book SynopsisFit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems.Introduction to Numerical Linear Algebra is ideal for a flipped classroom, as it provides detailed explanations that allow students to read on their own and instructors to go beyond lecturing, assumes that the reader has taken a course on linear algebra, but reviews background as needed, and covers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, a detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration, a discussion of the use of the SVD for assigning grades, and multigrid methods. This textbook is appropriate for undergraduate and beginning graduate students in mathematics and related fields. It can be used in the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory

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Book SynopsisThis expansive volume describes the history of numerical methods proposed to solve linear algebra problems,, from antiquity to the present day. The authors focus on methods for solving linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of the main important contributors to the field.A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, and to applied mathematiciansas well as to and historians of mathematics as well.

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Book SynopsisReduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications.This book will be of interest to researchers and graduate students in the field of reduced order modeling.

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Book SynopsisRounding Errors in Algebraic Processes was the first book to give systematic analyses of the effects of rounding errors on a variety of key computations involving polynomials and matrices.A detailed analysis is given of the rounding errors made in the elementary arithmetic operations and inner products, for both floating-point arithmetic and fixed-point arithmetic. The results are then applied in the error analyses of a variety of computations involving polynomials as well as the solution of linear systems, matrix inversion, and eigenvalue computations.The conditioning of these problems is investigated. The aim was to provide a unified method of treatment, and emphasis is placed on the underlying concepts.This book is intended for mathematicians, computer scientists, those interested in the historical development of numerical analysis, and students in numerical analysis and numerical linear algebra.Trade Review[This book] combines a rigorous mathematical analysis with a practicality that stems from an obvious first-hand contact with the actual numerical computation. The well-chosen examples alone show vividly both the importance of the study of rounding errors and the perils of its neglect. A. A. Grau, SIAM Review (1966)

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Book SynopsisDivided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to differential geometry, Fourier series, differential equations, and other subjects. The first section of Classical Analysis of Real-Valued Functions covers the theorems of existence of supremum and infimum of bounded sets on the real line and the Lagrange formula for differentiable functions. Applications of these results are crucial for classical mathematical analysis, andmany are threaded through the text. In the second part of the book, the implicit function theorem plays a central role, while the Gauss–Ostrogradskii formula, surface integration, Heine–Borel lemma, the Ascoli–Arzelà theorem, and the one-dimensional indefinite Lebesgue integral are also covered. This book is intended for students in the first and second years of classical universities majoring in pure and applied mathematics, but students of engineering disciplines will also gain important and helpful insights. It is appropriate for courses in mathematical analysis, functional analysis, real analysis, and calculus and can be used for self-study as well.

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Book SynopsisThis book presents in comprehensive detail numerical solutions to boundary value problems of a number of differential equations using the so-called Shooting Method. 4th order Runge-Kutta method, Newton's forward difference interpolation method and bisection method for root finding have been employed in this regard. Programs in Mathematica 6.0 were written to obtain the numerical solutions. This monograph on Shooting Method is the only available detailed resource of the topic.Table of ContentsPreface; Introduction; Differential Equations of Some Elementary Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method; Differential Equations of Special Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method; Differential Equation of Airy Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method; Differential Equation of Stationary Localized Wavepacket: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method; Differential Equation for Motion under Gravitational Interaction: Numerical Solution of Boundary Value Problem with So-Called Shooting Method; Conclusion; References; Index.

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Book SynopsisTriangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena. In numerical simulations, the functional spaces of approximation used to search for solutions are defined from meshes, and in this sense these meshes play a fundamental role. This strong link between the meshes and functional spaces leads us to consider advanced simulation methods in which the meshes are adapted to the behaviors of the underlying physical phenomena. This book presents the basic elements of this meshing vision.Table of ContentsForeword 9 Introduction 11 Chapter 1 Finite Elements and Shape Functions 15 1.1. Basic concepts 15 1.2. Shape functions, complete elements 18 1.2.1. Generic expression of shape functions 18 1.2.2. Explicit expression for degrees 1–3 22 1.3. Shape functions, reduced elements 26 1.3.1. Simplices, triangles and tetrahedra 27 1.3.2. Tensor elements, quadrilateral and hexahedral elements 31 1.3.3. Other elements, prisms and pyramids 48 1.4. Shape functions, rational elements 49 1.4.1. Rational triangle with a degree of 2 or arbitrary degree 49 1.4.2. Rational quadrilateral of an arbitrary degree 50 1.4.3. General case, B-splines or Nurbs elements 50 Chapter 2 Lagrange and Bézier Interpolants 53 2.1. Lagrange–Bézier analogy 54 2.2. Lagrange functions expressed in Bézier forms 55 2.2.1. The case of tensors, natural coordinates 55 2.2.2. Simplicial case, barycentric coordinates 63 2.3. Bézier polynomials expressed in Lagrangian form 66 2.4. Application to curves 66 2.4.1. Bézier expression for a Lagrange curve 67 2.4.2. Lagrangian expression for a Bézier curve 70 2.5. Application to patches 71 2.5.1. Bézier expression for a patch in Lagrangian form 71 2.5.2. Lagrangian expression for a patch in Bézier form 73 2.6. Reduced elements 74 2.6.1. The tensor case, Bézier expression for a reduced Lagrangian patch 74 2.6.2. The tensor case, definition of reduced Bézier patches 82 2.6.3. The tensor case, Lagrangian expression of a reduced Bézier patch 90 2.6.4. The case of simplices 92 Chapter 3 Geometric Elements and Geometric Validity 95 3.1. Two-dimensional elements 96 3.2. Surface elements 105 3.3. Volumetric elements 105 3.4. Control points based on nodes 111 3.5. Reduced elements 115 3.5.1. Simplices, triangles and tetrahedra 115 3.5.2. Tensor elements, quadrilaterals and hexahedra 116 3.5.3. Other elements, prisms and pyramids 120 3.6. Rational elements 121 3.6.1. Shift from Lagrange rationals to Bézier rationals 121 3.6.2. Degree 2, working on the (arc of a) circle 121 3.6.3. Application to the analysis of rational elements 123 3.6.4. On the use of rational elements or more 138 Chapter 4 Triangulation 141 4.1. Triangulation, definitions, basic concepts and natural entities 142 4.1.1. Definitions and basic concepts 142 4.1.2. Natural entities 145 4.1.3. A ball (topological) of a vertex 145 4.1.4 A shell of a k-face 145 4.1.5 The ring of a k-face 146 4.2. Topology and local topological modifications 146 4.2.1. Flipping an edge in two dimensions 148 4.2.2. Flipping a face in three dimensions 148 4.2.3. Flipping an edge in three dimensions 148 4.2.4. Other flips? 150 4.3. Enriched data structures 151 4.3.1. Minimal structure 151 4.3.2. Enriched structure 152 4.4. Construction of natural entities 153 4.5. Triangulation, construction methods 156 4.6. The incremental method, a generic method 159 4.6.1. Naive triangulation 160 4.6.2. Delaunay triangulation 163 Chapter 5 Delaunay Triangulation 165 5.1. History 166 5.2. Definitions and properties 168 5.3. The incremental method for Delaunay 175 5.4. Other methods of construction 181 5.5. Variants 186 5.6. Anisotropy 188 Chapter 6 Triangulation and Constraints 193 6.1. Triangulation of a domain 194 6.1.1. Triangulation of a domain in two dimensions 195 6.1.2. Triangulation of a domain in three dimensions 202 6.2. Delaunay Triangulation “Delaunay admissibility” 214 6.3. Triangulation of a variety 219 6.4. Topological invariants (triangles and tetrahedra) 222 Chapter 7 Geometric Modeling: Methods 233 7.1. Implicit or explicit form (CAD), starting from an analytical definition 234 7.1.1. Modeling an implicit curve, continuous → discrete 234 7.1.2. Modeling a parametric curve 237 7.1.3. Modeling an implicit surface 238 7.1.4. Modeling of a parametric surface 242 7.2. Starting from a discretization or triangulation, discrete → continuous 246 7.2.1. Case of a curve 247 7.2.2. The case of a surface 253 7.3. Starting from a point cloud, discrete → discrete 278 7.3.1. The case of a curve in two dimensions 278 7.3.2. The case of a surface 283 7.4. Extraction of characteristic points and characteristic lines 302 Chapter 8 Geometric Modeling: Examples 305 8.1. Geometric modeling of parametric patches 306 8.2. Characteristic lines of a discrete surface 311 8.3. Parametrization of a surface patch through unfolding 311 8.4. Geometric simplification of a surface triangulation 324 8.5. Geometric support for a discrete surface 325 8.6. Discrete reconstruction of a digitized object or environment 330 Chapter 9 A Few Basic Algorithms and Formulae 343 9.1. Subdivision of an entity (De Casteljau) 344 9.1.1. Subdivision of a curve 344 9.1.2. Subdivision of a patch 345 9.2. Computing control coefficients (higher order elements) 348 9.3. Algorithms for the insertion of a point (Delaunay) 351 9.3.1. Classic algorithm 352 9.3.2. Modified algorithms 355 9.4. Construction of neighboring relationships, balls and shells 357 9.4.1. Neighboring relationships 357 9.4.2. Construction of the ball of a vertex 359 9.4.3. Construction of the shell of an edge 361 9.5. Localization problems 363 9.5.1. Triangulations or simplicial meshes 363 9.5.2. Other meshes 367 9.6. Some formulae 367 Conclusions and Perspectives 369 Bibliography 371 Index 377

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Book SynopsisThree-dimensional surface meshes are the most common discrete representation of the exterior of a virtual shape. Extracting relevant geometric or topological features from them can simplify the way objects are looked at, help with their recognition, and facilitate description and categorization according to specific criteria. This book adopts the point of view of discrete mathematics, the aim of which is to propose discrete counterparts to concepts mathematically defined in continuous terms. It explains how standard geometric and topological notions of surfaces can be calculated and computed on a 3D surface mesh, as well as their use for shape analysis. Several applications are also detailed, demonstrating that each of them requires specific adjustments to fit with generic approaches. The book is intended not only for students, researchers and engineers in computer science and shape analysis, but also numerical geologists, anthropologists, biologists and other scientists looking for practical solutions to their shape analysis, understanding or recognition problems.Table of ContentsPreface ix Introduction xi Chapter 1. Geometric Features based on Curvatures 1 1.1. Introduction 1 1.2. Some mathematical reminders of the differential geometry of surfaces 2 1.2.1. Fundamental forms and normal curvature 2 1.2.2. Principal curvatures and shape index 5 1.2.3. Principal directions and lines of curvature 6 1.2.4. Weingarten equations and shape operator 9 1.2.5. Practical computation of differential parameters 12 1.2.6. Euler’s theorem 13 1.2.7. Meusnier’s theorem 15 1.2.8. Local approximation of the surface 16 1.2.9. Focal surfaces 17 1.3. Computation of differential parameters on a discrete 3D mesh 19 1.3.1. Introduction 19 1.3.2. Some notations 19 1.3.3. Computing normal vectors 20 1.3.4. Locally fitting a parametric surface 22 1.3.5. Discrete differential geometry operators 22 1.3.6. Integrating 2D curvatures 28 1.3.7. Tensor of curvature: Taubin’s formula 28 1.3.8. Tensor of curvature based on the normal cycle theory 30 1.3.9. Integral estimators 34 1.3.10. Processing unstructured 3D point clouds 38 1.3.11. Discussion of the methods 38 1.4. Feature line extraction 46 1.4.1. Introduction 46 1.4.2. Lines of curvature 47 1.4.3. Crest/ridge lines 55 1.4.4. Feature lines based on homotopic thinning 79 1.5. Region-based approaches 84 1.5.1. Mesh segmentation 84 1.5.2. Shape description based on graphs 87 1.6. Conclusion 98 Chapter 2. Topological Features 99 2.1. Mathematical background 99 2.1.1. A topological view on surfaces 100 2.1.2. Algebraic topology 103 2.2. Computation of global topological features 106 2.2.1. Connected components and genus 106 2.2.2. Homology groups 107 2.3. Combining geometric and topological features 111 2.3.1. Persistent homology 112 2.3.2. Reeb graph and Morse–Smale complex 115 2.3.3. Homology generators 118 2.3.4. Measuring holes 121 2.4. Conclusion 128 Chapter 3. Applications 131 3.1. Introduction 131 3.2. Medicine: lines of curvature for polyp detection in virtual colonoscopy 131 3.3. Paleo-anthropology: crest/ridge lines for shape analysis of human fossils 133 3.4. Geology: extraction of fracture lines on virtual outcrops 137 3.5. Planetary science: detection of feature lines for the extraction of impact craters on asteroids and rocky planets 140 3.6. Botany: persistent homology to recover the branching structure of plants 143 Conclusion 145 References 149 Index 169

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Book SynopsisEarthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi-)Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7.Table of ContentsList of Abbreviations ix List of Symbols xi Preface xv Introduction xix Chapter 1. Fundamentals on Stress Changes 1 1.1. Introduction 1 1.2. Stress interaction 4 1.3. Stress changes calculation 12 1.4. Modeling of Coulomb stress changes for different faulting types 15 1.4.1.ΔCS for strike-slip faulting 15 1.4.2.ΔCS for dip-slip faulting 16 1.5. Seismicity triggered by stress transfer 21 1.5.1. Triggering of strong earthquakes 21 1.5.2. Aftershock triggering 23 1.5.3. Triggering of mining seismicity 28 1.6. Discussion on stress interaction 31 Chapter 2. Hidden Markov Models 35 2.1. Introduction 35 2.2. Hidden Markov framework 37 2.3. Seismotectonic regime and seismicity data 42 2.4. Application to earthquake occurrences 44 2.4.1. Two hidden states and three observation types 45 2.4.2. Three hidden states and three observation types 48 2.4.3. Model selection and simulation 50 2.4.4. Steps number for the first earthquake occurrence 53 2.5. Conclusion 54 Chapter 3. Hidden Markov Renewal Models 57 3.1. Introduction 57 3.2. Semi-Markov framework 58 3.3. Hidden Markov renewal framework 65 3.4. Modeling earthquakes in Greece 66 3.4.1. Hitting times and earthquake occurrence numbers 69 3.5. Conclusion 73 Chapter 4. Hitting Time Intensity 75 4.1. Introduction 75 4.2. DTIHT for semi-Markov chains 76 4.2.1. Statistical estimation of the DTIHT 78 4.3. DTIHT for hidden Markov renewal chains 83 4.3.1. Statistical estimation of the DTIHT 85 4.4. Conclusion 87 Chapter 5. Models Comparison 89 5.1. Introduction 89 5.2. Markov framework 90 5.2.1. HMM case 92 5.2.2. HMRM case 92 5.3. Markov renewal framework 93 5.3.1. HMM case 95 5.3.2. HMRM case 96 5.4. Conclusion 97 Discussion & Concluding Remarks 99 Appendices 105 Appendix 1 107 Appendix 2 113 Appendix 3 117 References 119 Index 137

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Book SynopsisThe purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing. This last refers to the implementation of appropriate approaches to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or of engineering (mechanics of structures, mechanics of fluids, treatment signal, etc.). Each chapter of this book recalls the essence of the different methods resolution and presents several applications in the field of engineering as well as programs developed under Matlab software.Table of ContentsPreface ix Part 1. Solving Equations 1 Chapter 1. Solving Nonlinear Equations 3 1.1 Introduction 3 1.2 Separating the roots 3 1.3 Approximating a separated root 4 1.3.1 Bisection method (or dichotomy method) 4 1.3.2 Fixed-point method 6 1.3.3 First convergence criterion 7 1.3.4 Iterative stopping criteria.8 1.3.5 Second convergence criterion (local criterion) 9 1.3.6 Newton’s method (or the method of tangents) 10 1.3.7 Secant method 12 1.3.8 Regula falsi method (or false position method) 17 1.4 Order of an iterative process.19 1.5 Using Matlab 19 1.5.1 Finding the roots of polynomials 19 1.5.2 Bisection method 21 1.5.3 Newton’s method 22 Chapter 2. Numerically Solving Differential Equations 25 2.1 Introduction 25 2.2 Cauchy problem and discretization 27 2.3 Euler’s method 30 2.3.1 Interpretation 30 2.3.2 Convergence 30 2.4 One-step Runge–Kutta method 31 2.4.1 Second-order Runge–Kutta method 32 2.4.2 Fourth-order Runge–Kutta method 33 2.5 Multi-step Adams methods 36 2.5.1 Open Adams methods 36 2.5.2 Closed Adams formulas 39 2.6 Predictor–Corrector method.41 2.7 Using Matlab 43 Part 2. Solving PDEs 47 Chapter 3. Finite Difference Methods 49 3.1 Introduction 49 3.2 Presentation of the finite difference method 51 3.2.1 Convergence, consistency and stability 53 3.2.2 Courant–Friedrichs–Lewy condition 56 3.2.3 Von Neumann stability analysis 57 3.3 Hyperbolic equations 58 3.3.1 Key results 59 3.3.2 Numerical schemes for solving the transport equation 63 3.3.3 Wave equation 66 3.3.4 Burgers equation 68 3.4 Elliptic equations 72 3.4.1 Poisson equation 72 3.5 Parabolic equations 74 3.5.1 Heat equation 74 3.6 Using Matlab 76 Chapter 4. Finite Element Method 83 4.1 Introduction 83 4.2 One-dimensional finite element methods 83 4.3 Two-dimensional finite element methods 88 4.4 General procedure of the method 93 4.5 Finite element method for computing elastic structures 93 4.5.1 Linear elasticity 93 4.5.2 Variational formulation of the linear elasticity problem 97 4.5.3 Planar linear elasticity problems 99 4.5.4 Applying the finite element method to planar problems 101 4.5.5 Axisymmetric problems.105 4.5.6 Three-dimensional problems 107 4.6 Using Matlab 107 4.6.1 Solving Poisson’s equation 108 4.6.2 Solving the heat equation.111 4.6.3 Computing structures 112 Chapter 5. Finite Volume Methods 117 5.1 Introduction 117 5.2 Finite volume method (FVM) 118 5.2.1 Conservation properties of the method 118 5.2.2 The stages of the method.119 5.2.3 Convergence 120 5.2.4 Consistency 120 5.2.5 Stability 120 5.3 Advection schemes 121 5.3.1 Two-dimensional FVM. 126 5.3.2 Convection-diffusion equation 129 5.3.3 Central differencing scheme 131 5.3.4 Upwind (decentered) scheme 133 5.3.5 Hybrid scheme 136 5.3.6 Power-law scheme 136 5.3.7 QUICK scheme 137 5.3.8 Higher-order schemes 139 5.3.9 Unsteady one-dimensional convection-diffusion Equation 140 5.3.10 Explicit scheme 142 5.3.11 Crank–Nicolson scheme.142 5.3.12 Implicit scheme 143 5.4 Using Matlab 144 Chapter 6. Meshless Methods. 147 6.1 Introduction 147 6.2 Limitations of the FEM and motivation of meshless methods 148 6.3 Examples of meshless methods148 6.3.1 Advantages of meshless methods 149 6.3.2 Disadvantages of meshless methods150 6.3.3 Comparison of the finite element method and meshless methods 151 6.4 Basis of meshless methods 151 6.4.1 Approximations 151 6.4.2 Kernel (weight) functions.152 6.4.3 Completeness 152 6.4.4 Partition of unity 152 6.5 Meshless method (EFG) 153 6.5.1 Theory 153 6.5.2 Moving Least-Squares Approximation 153 6.6 Application of the meshless method to elasticity 163 6.6.1 Formulation of static linear elasticity 163 6.6.2 Imposing essential boundary conditions 165 6.7 Numerical examples 170 6.7.1 Fixed-free beam 170 6.7.2 Compressed block 171 6.8 Using Matlab 173 Part 3. Appendices 179 Appendix 1181 Appendix 2189 Bibliography 195 Index 199

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Book SynopsisThis book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences.The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus.The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.Table of ContentsIntroduction 1 0.1 The finite element method 1 0.1.1 General remarks 1 0.1.2 Historical evolution of the method 2 0.1.3 State of the art 3 0.2 Object and organization of the book 3 0.2.1 Teaching the finite element method 3 0.2.2 Objectives of the book 4 0.2.3 Organization of the book 4 0.3 Numerical modeling approach 6 0.3.1 General aspects 6 0.3.2 Physical model 7 0.3.3 Mathematical model 9 0.3.4 Numerical model 10 0.3.5 Computer model 13 Bibliography 16 Conference proceedings 17 Monographs 18 Periodicals 19 Chapter 1. Approximations with finite elements 21 1.0 Introduction 21 1.1 General remarks 21 1.1.1 Nodal approximation 21 1.1.2 Approximations with finite elements 28 1.2 Geometrical definition of the elements 33 1.2.1 Geometrical nodes 33 1.2.2 Rules for the partition of a domain into elements 33 1.2.3 Shapes of some classical elements 35 1.2.4 Reference elements 37 1.2.5 Shapes of some classical reference elements 41 1.2.6 Node and element definition tables 44 1.3 Approximation based on a reference element 45 1.3.1 Expression of the approximate function u(x) 45 1.3.2 Properties of approximate function u(x) 49 1.4 Construction of functions N (ξ ) and N (ξ ) 54 1.4.1 General method of construction 54 1.4.2 Algebraic properties of functions N and N 59 1.5 Transformation of derivation operators 61 1.5.1 General remarks 61 1.5.2 First derivatives 62 1.5.3 Second derivatives 65 1.5.4 Singularity of the Jacobian matrix 68 1.6 Computation of functions N, their derivatives and the Jacobian matrix 72 1.6.1 General remarks 72 1.6.2 Explicit forms for N 73 1.7 Approximation errors on an element 75 1.7.1 Notions of approximation errors 75 1.7.2 Error evaluation technique 80 1.7.3 Improving the precision of approximation 83 1.8 Example of application: rainfall problem 89 Bibliography 95 Chapter 2. Various types of elements 97 2.0 Introduction 97 2.1 List of the elements presented in this chapter 97 2.2 One-dimensional elements 99 2.2.1 Linear element (two nodes, C0) 99 2.2.2 High-precision Lagrangian elements: (continuity C0) 101 2.2.3 High-precision Hermite elements 105 2.2.4 General elements 109 2.3 Triangular elements (two dimensions) 111 2.3.1 Systems of coordinates 111 2.3.2 Linear element (triangle, three nodes, C0) 113 2.3.3 High-precision Lagrangian elements (continuity C0) 115 2.3.4 High-precision Hermite elements 123 2.4 Quadrilateral elements (two dimensions) 127 2.4.1 Systems of coordinates 127 2.4.2 Bilinear element (quadrilateral, 4 nodes, C0) 128 2.4.3 High-precision Lagrangian elements 129 2.4.4 High-precision Hermite element 134 2.5 Tetrahedral elements (three dimensions) 137 2.5.1 Systems of coordinates 137 2.5.2 Linear element (tetrahedron, four nodes, C0) 139 2.5.3 High-precision Lagrangian elements (continuity C0) 140 2.5.4 High-precision Hermite elements 142 2.6 Hexahedric elements (three dimensions) 143 2.6.1 Trilinear element (hexahedron, eight nodes, C0) 143 2.6.2 High-precision Lagrangian elements (continuity C0) 144 2.6.3 High-precision Hermite elements 150 2.7 Prismatic elements (three dimensions) 150 2.7.1 Element with six nodes (prism, six nodes, C0) 150 2.7.2 Element with 15 nodes (prism, 15 nodes, C0) 151 2.8 Pyramidal element (three dimensions) 152 2.8.1 Element with five nodes 152 2.9 Other elements 153 2.9.1 Approximation of vectorial values 153 2.9.2 Modifications of the elements 155 2.9.3 Elements with a variable number of nodes 156 2.9.4 Superparametric elements 158 2.9.5 Infinite elements 158 Bibliography 160 Chapter 3. Integral formulation 161 3.0 Introduction 161 3.1 Classification of physical systems 163 3.1.1 Discrete and continuous systems 163 3.1.2 Equilibrium, eigenvalue and propagation problems 164 3.2 Weighted residual method 172 3.2.1 Residuals 172 3.2.2 Integral forms 173 3.3 Integral transformations 174 3.3.1 Integration by parts 174 3.3.2 Weak integral form 177 3.3.3 Construction of additional integral forms 179 3.4 Functionals 182 3.4.1 First variation 182 3.4.2 Functional associated with an integral form 183 3.4.3 Stationarity principle 187 3.4.4 Lagrange multipliers and additional functionals 188 3.5 Discretization of integral forms 194 3.5.1 Discretization of W 194 3.5.2 Approximation of the functions u 197 3.5.3 Choice of the weighting functions ψ 198 3.5.4 Discretization of a functional (Ritz method) 205 3.5.5 Properties of the systems of equations 208 3.6 List of PDEs and weak expressions 209 3.6.1 Scalar field problems 210 3.6.2 Solid mechanics 213 3.6.3 Fluid mechanics 217 Bibliography 229 Chapter 4. Matrix presentation of the finite element method 231 4.0 Introduction 231 4.1 The finite element method 231 4.1.1 Finite element approach 231 4.1.2 Conditions for convergence of the solution 243 4.1.3 Patch test 256 4.2 Discretized elementary integral forms We 264 4.2.1 Matrix expression of We 264 4.2.2 Case of a nonlinear operator L 267 4.2.3 Integral form We on the reference element 269 4.2.4 A few classic forms of We and of elementary matrices 274 4.3 Techniques for calculating elementary matrices 274 4.3.1 Explicit calculation for a triangular element (Poisson’s equation) 274 4.3.2 Explicit calculation for a quadrangular element (Poisson’s equation) 279 4.3.3 Organization of the calculation of the elementary matrices by numerical integration 280 4.3.4 Calculation of the elementary matrices: linear problems 282 4.4 Assembly of the global discretized form W 297 4.4.1 Assembly by expansion of the elementary matrices 298 4.4.2 Assembly in structural mechanics 303 4.5 Technique of assembly 305 4.5.1 Stages of assembly 305 4.5.2 Rules of assembly 305 4.5.3 Example of a subprogram for assembly 307 4.5.4 Construction of the localization table LOCE 308 4.6 Properties of global matrices 310 4.6.1 Band structure 310 4.6.2 Symmetry 314 4.6.3 Storage methods 314 4.7 Global system of equations 318 4.7.1 Expression of the system of equations 318 4.7.2 Introduction of the boundary conditions 318 4.7.3 Reactions 321 4.7.4 Transformation of variables 321 4.7.5 Linear relations between variables 323 4.8 Example of application: Poisson’s equation 324 4.9 Some concepts about convergence, stability and error calculation 329 4.9.1 Notations 329 4.9.2 Properties of the exact solution 330 4.9.3 Properties of the solution obtained by the finite element method 331 4.9.4 Stability and locking 334 4.9.5 One-dimensional exact finite elements 337 Bibliography 343 Chapter 5. Numerical Methods 345 5.0 Introduction 345 5.1 Numerical integration 346 5.1.1 Introduction 346 5.1.2 One-dimensional numerical integration 348 5.1.3 Two-dimensional numerical integration 360 5.1.4 Numerical integration in three dimensions 368 5.1.5 Precision of integration 372 5.1.6 Choice of number of integration points 375 5.1.7 Numerical integration codes 379 5.2 Solving systems of linear equations 384 5.2.1 Introduction 384 5.2.2 Gaussian elimination method 385 5.2.3 Decomposition 391 5.2.4 Adaptation of algorithm (5.44) to the case of a matrix stored by the skyline method 399 5.3 Solution of nonlinear systems 404 5.3.1 Introduction 404 5.3.2 Substitution method 407 5.3.3 Newton–Raphson method 411 5.3.4 Incremental (or step-by-step) method 420 5.3.5 Changing of independent variables 421 5.3.6 Solution strategy 424 5.3.7 Convergence of an iterative method 426 5.4 Resolution of unsteady systems 429 5.4.1 Introduction 429 5.4.2 Direct integration methods for first-order systems 431 5.4.3 Modal superposition method for first-order systems 463 5.4.4 Methods for direct integration of second-order systems 466 5.4.5 Modal superposition method for second-order systems 476 5.5 Methods for calculating the eigenvalues and eigenvectors 480 5.5.1 Introduction 480 5.5.2 Recap of some properties of eigenvalue problems 481 5.5.3 Methods for calculating the eigenvalues 488 Bibliography 502 Chapter 6. Programming technique 505 6.0 Introduction 505 6.1 Functional blocks of a finite element program 506 6.2 Description of a typical problem 507 6.3 General programs 508 6.3.1 Possibilities of general programs 508 6.3.2 Modularity 511 6.4 Description of the finite element code 512 6.4.1 Introduction 512 6.4.2 General organization 513 6.4.3 Description of tables and variables 517 6.5 Library of elementary finite element method programs 521 6.5.1 Functional blocks 521 6.5.2 List of thermal elements 530 6.5.3 List of elastic elements 538 6.5.4 List of elements for fluid mechanics 545 6.6 Examples of application 549 6.6.1 Heat transfer problems 550 6.6.2 Planar elastic problems 558 6.6.3 Fluid flow problems 566 Appendix. Sparse solver 577 7.0 Introduction 577 7.1 Methodology of the sparse solver 578 7.1.1 Assembly of matrices in sparse form: row-by-row format 579 7.1.2 Permutation using the “minimum degree” algorithm 584 7.1.3 Modified column–column storage format 587 7.1.4 Symbolic factorization 589 7.1.5 Numerical factorization 590 7.1.6 Solution of the system by descent/ascent 592 7.2 Numerical examples 593 Bibliography 595 Index 597

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Book SynopsisThis book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.Trade Review"The book is very carefully written, in a reader-friendly style. It can be considered as an introductory textbook for the theory of ill-posed problems and their numerical solution." (Mathematical Reviews/MathSciNet 11/05/2017)Table of ContentsPreface ix Part 1. Introduction and Examples 1 Chapter 1. Overview of Inverse Problems 3 1.1. Direct and inverse problems 3 1.2. Well-posed and ill-posed problems 4 Chapter 2. Examples of Inverse Problems 9 2.1. Inverse problems in heat transfer 10 2.2. Inverse problems in hydrogeology 13 2.3. Inverse problems in seismic exploration 16 2.4. Medical imaging 21 2.5. Other examples 25 Part 2. Linear Inverse Problems 29 Chapter 3. Integral Operators and Integral Equations 31 3.1. Definition and first properties 31 3.2. Discretization of integral equations 36 3.2.1. Discretization by quadrature–collocation 36 3.2.2. Discretization by the Galerkin method 39 3.3. Exercises 42 Chapter 4. Linear Least Squares Problems – Singular Value Decomposition 45 4.1. Mathematical properties of least squares problems 45 4.1.1. Finite dimensional case 50 4.2. Singular value decomposition for matrices 52 4.3. Singular value expansion for compact operators 57 4.4. Applications of the SVD to least squares problems 60 4.4.1. The matrix case 60 4.4.2. The operator case 63 4.5. Exercises 65 Chapter 5. Regularization of Linear Inverse Problems 71 5.1. Tikhonov’s method 72 5.1.1. Presentation 72 5.1.2. Convergence 73 5.1.3. The L-curve 81 5.2. Applications of the SVE 83 5.2.1. SVE and Tikhonov’s method 84 5.2.2. Regularization by truncated SVE 85 5.3. Choice of the regularization parameter 88 5.3.1. Morozov’s discrepancy principle 88 5.3.2. The L-curve 91 5.3.3. Numerical methods 92 5.4. Iterative methods 94 5.5. Exercises 98 Part 3. Nonlinear Inverse Problems 103 Chapter 6. Nonlinear Inverse Problems – Generalities 105 6.1. The three fundamental spaces 106 6.2. Least squares formulation 111 6.2.1. Difficulties of inverse problems 114 6.2.2. Optimization, parametrization, discretization 114 6.3. Methods for computing the gradient – the adjoint state method 116 6.3.1. The finite difference method 116 6.3.2. Sensitivity functions 118 6.3.3. The adjoint state method 119 6.3.4. Computation of the adjoint state by the Lagrangian 120 6.3.5. The inner product test 123 6.4. Parametrization and general organization 123 6.5. Exercises 125 Chapter 7. Some Parameter Estimation Examples 127 7.1. Elliptic equation in one dimension 127 7.1.1. Computation of the gradient 128 7.2. Stationary diffusion: elliptic equation in two dimensions 129 7.2.1. Computation of the gradient: application of the general method 132 7.2.2. Computation of the gradient by the Lagrangian 134 7.2.3. The inner product test 135 7.2.4. Multiscale parametrization 135 7.2.5. Example 136 7.3. Ordinary differential equations 137 7.3.1. An application example 144 7.4. Transient diffusion: heat equation 147 7.5. Exercises 152 Chapter 8. Further Information 155 8.1. Regularization in other norms 155 8.1.1. Sobolev semi-norms 155 8.1.2. Bounded variation regularization norm 157 8.2. Statistical approach: Bayesian inversion 157 8.2.1. Least squares and statistics 158 8.2.2. Bayesian inversion 160 8.3. Other topics 163 8.3.1. Theoretical aspects: identifiability 163 8.3.2. Algorithmic differentiation . 163 8.3.3. Iterative methods and large-scale problems 164 8.3.4. Software 164 Appendices 167 Appendix 1 169 Appendix 2 183 Appendix 3 193 Bibliography 205 Index 213

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Book SynopsisBiometrics, the science of using physical traits to identify individuals, is playing an increasing role in our security-conscious society and across the globe. Biometric authentication, or bioauthentication, systems are being used to secure everything from amusement parks to bank accounts to military installations. Yet developments in this field have not been matched by an equivalent improvement in the statistical methods for evaluating these systems. Compensating for this need, this unique text/reference provides a basic statistical methodology for practitioners and testers of bioauthentication devices, supplying a set of rigorous statistical methods for evaluating biometric authentication systems. This framework of methods can be extended and generalized for a wide range of applications and tests. This is the first single resource on statistical methods for estimation and comparison of the performance of biometric authentication systems. The book focuses on six common performance metrics: for each metric, statistical methods are derived for a single system that incorporates confidence intervals, hypothesis tests, sample size calculations, power calculations and prediction intervals. These methods are also extended to allow for the statistical comparison and evaluation of multiple systems for both independent and paired data. Topics and features: * Provides a statistical methodology for the most common biometric performance metrics: failure to enroll (FTE), failure to acquire (FTA), false non-match rate (FNMR), false match rate (FMR), and receiver operating characteristic (ROC) curves * Presents methods for the comparison of two or more biometric performance metrics * Introduces a new bootstrap methodology for FMR and ROC curve estimation * Supplies more than 120 examples, using publicly available biometric data where possible * Discusses the addition of prediction intervals to the bioauthentication statistical toolset * Describes sample-size and power calculations for FTE, FTA, FNMR and FMR Researchers, managers and decisions makers needing to compare biometric systems across a variety of metrics will find within this reference an invaluable set of statistical tools. Written for an upper-level undergraduate or master’s level audience with a quantitative background, readers are also expected to have an understanding of the topics in a typical undergraduate statistics course. Dr. Michael E. Schuckers is Associate Professor of Statistics at St. Lawrence University, Canton, NY, and a member of the Center for Identification Technology Research.Table of ContentsPart I: Introduction Introduction Statistical Background Part II: Primary Matching and Classification Measures False Non-Match Rate False Match Rate Receiver Operating Characteristic Curve and Equal Error Rate Part III: Biometric Specific Measures Failure to Enrol Failure to Acquire Part IV: Additional Topics and Appendices Additional Topics and Discussion Tables

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Book SynopsisThis volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text.Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful. Trade Review“The book can be of special interest to mathematicians, STEM students, and engineers working in multidisciplinary industry settings where the insight provided by differential-algebraic equations can be determinant in decision making.” (Andrzej Sokolowski, MAA Reviews, August 11, 2019)Table of ContentsGeneral Nonlinear Differential Algebraic Equations and Tracking Problems: A Robotics Example.- DAE Aspects in Vehicle Dynamics and Mobile Robotics.- Open-loop Control of Underactuated Mechanical Systems Using Servo-constraints: Analysis and Some Examples.- Systems of Differential Algebraic Equations in Computational Electromagnetics.- Gas Network Benchmark Models.- Topological Index Analysis Applied to Coupled Flow Networks.- Nonsmooth DAEs with Applications in Modeling Phase Changes.- Continuous, Semi-Discrete, and Fully Discretized Navier-Stokes Equations.

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Book SynopsisThis textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.Trade Review“This book is an excellent first course in approximation theory, covering all the aspects from theoretical results to practical methods, from discrete to continuous approximation, from univariate to multivariate. … The book is an excellent text for an undergraduate course in approximation methods. … this book is a very important textbook on approximation theory and its methods.” (Ana Cristina Matos, Mathematical Reviews, August, 2019)Table of Contents1 Introduction.- 2 Basic Methods and Numerical Analysis.- 3 Best Approximations.- 4 Euclidean Approximations.- 5 Chebyshev Approximations.- 6 Asymptotic Results.- 7 Basic Concepts of Signal Approximation.- 8 Kernel-Based Approximation.- 9 Computational Topology.- References.- Subject Index.- Name Index.

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Book SynopsisThis book constitutes the proceedings of the 18th International Conference on Unconventional Computation and Natural Computation, UCNC 2019, held in Tokyo, Japan, in June 2019.The 19 full papers presented were carefully reviewed and selected from 32 submissions. The papers cover topics such as hypercomputation; chaos and dynamical systems based computing; granular, fuzzy and rough computing; mechanical computing; cellular, evolutionary, molecular, neural, and quantum computing; membrane computing; amorphous computing, swarm intelligence; artificial immune systems; physics of computation; chemical computation; evolving hardware; the computational nature of self-assembly, developmental processes, bacterial communication, and brain processes.Table of ContentsInvited Paper.- Co-designing the computational model and the computing substrate.- Contributed Papers.- Generalized Membrane Systems with Dynamical Structure, Petri Nets, and Multiset Approximation Spaces.- Quantum Dual Adversary for Hidden Subgroups and Beyond.- Further Properties of Self-assembly by Hairpin Formation.- The Role of Structure and Complexity on Reservoir Computing Quality.- Lindenmayer Systems and Global Transformations.- Swarm-based multiset rewriting computing models.- DNA Origami Words and Rewriting Systems.- Computational Limitations of Affine Automata.- An Exponentially Growing Nubot System Without State Changes.- Impossibility of Sufficiently Simple Chemical Reaction Network Implementations in DNA Strand Displacement.- Quantum Algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs.- Viewing rate-based neurons as biophysical conductance outputting models.- The Lyapunov Exponents of Reversible Cellular Automata Are Uncomputable.- Geometric Tiles and Powers and Limitations of Geometric Hindrance in Self-Assembly.- DNA Computing Units Based on Fractional Coding.- The role of the representational entity in physical computing.- OIM: Oscillator-based Ising Machines for Solving Combinatorial Optimisation Problems.- Relativizations of Nonuniform Quantum Finite Automata Families.- Self-stabilizing Gellular Automata.

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Book SynopsisThis textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications.Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry.Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics.Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.Trade Review“The book … is intended ‘for a wide audience ranging from upper undergraduate to advanced graduate students in mathematics, physics, and more broadly engineering students, especially in computer science.’ … The text’s coverage is extensive, its exposition clear throughout, and the color illustrations helpful. The authors are also familiar with many texts at a comparable level and have drawn on them in several places to include some of the most insightful proofs already in the literature.” (Jer-Chin Chuang, MAA Reviews, October 4, 2021)“The book is intended for incremental study and covers both basic concepts and more advanced ones. The former are thoroughly supported with theory and examples, and the latter are backed up with extensive reading lists and references. … Thanks to its design and approach style this is a timely and much needed addition that enables interdisciplinary bridges and the discovery of new applications for differential geometry.” (Corina Mohorian, zbMATH 1453.53001, 2021)Table of Contents1. The Matrix Exponential; Some Matrix Lie Groups.- 2. Adjoint Representations and the Derivative of exp.- 3. Introduction to Manifolds and Lie Groups.- 4. Groups and Group Actions.- 5. The Lorentz Groups ⊛.- 6. The Structure of O(p,q) and SO(p, q).- 7. Manifolds, Tangent Spaces, Cotangent Spaces.- 8. Construction of Manifolds From Gluing Data ⊛.- 9. Vector Fields, Integral Curves, Flows.- 10. Partitions of Unity, Covering Maps ⊛.- 11. Basic Analysis: Review of Series and Derivatives.- 12. A Review of Point Set Topology.-13. Riemannian Metrics, Riemannian Manifolds.- 14. Connections on Manifolds.- 15. Geodesics on Riemannian Manifolds.- 16. Curvature in Riemannian Manifolds.- 17. Isometries, Submersions, Killing Vector Fields.- 18. Lie Groups, Lie Algebra, Exponential Map.- 19. The Derivative of exp and Dynkin's Formula ⊛.- 20. Metrics, Connections, and Curvature of Lie Groups.- 21. The Log-Euclidean Framework.- 22. Manifolds Arising from Group Actions.

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Book SynopsisThis volume gathers the latest advances and innovations in the field of flow-induced vibration and noise, as presented by leading international researchers at the 3rd International Symposium on Flow Induced Noise and Vibration Issues and Aspects (FLINOVIA), which was held in Lyon, France, in September 2019. It explores topics such as turbulent boundary layer-induced vibration and noise, tonal noise, noise due to ingested turbulence, fluid-structure interaction problems, and noise control techniques. The authors’ backgrounds represent a mix of academia, government, and industry, and several papers include applications to important problems for underwater vehicles, aerospace structures and commercial transportation. The book offers a valuable reference guide for all those interested in measurement, modelling, simulation and reproduction of the flow excitation and flow induced structural response.Table of ContentsSource Modeling.- Experimental Techniques.- Analytical Developments.- Numerical Methods.

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Book SynopsisThe book originates from the mini-symposium "Mathematical descriptions of traffic flow: micro, macro and kinetic models" organised by the editors within the ICIAM 2019 Congress held in Valencia, Spain, in July 2019. The book is composed of five chapters, which address new research lines in the mathematical modelling of vehicular traffic, at the cutting edge of contemporary research, including traffic automation by means of autonomous vehicles. The contributions span the three most representative scales of mathematical modelling: the microscopic scale of particles, the mesoscopic scale of statistical kinetic description and the macroscopic scale of partial differential equations.The work is addressed to researchers in the field.Table of ContentsM. Herty et al., Reconstruction of traffic speed distributions from kinetic models with uncertainties.- M. Herty et al., From kinetic to macroscopic models and back.- R. Ramadan et al., Structural Properties of the Stability of Jamitons.- C. Balzotti and E. Iacomini, Stop-and-go waves: A Microscopic and a Macroscopic Description.- F. A. Chiarello, An overview of non-local traffic flow models.

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Book SynopsisThis book presents a system that combines the expertise of four algorithms, namely Gradient Tree Boosting, Logistic Regression, Random Forest and Support Vector Classifier to trade with several cryptocurrencies. A new method for resampling financial data is presented as alternative to the classical time sampled data commonly used in financial market trading. The new resampling method uses a closing value threshold to resample the data creating a signal better suited for financial trading, thus achieving higher returns without increased risk. The performance of the algorithm with the new resampling method and the classical time sampled data are compared and the advantages of using the system developed in this work are highlighted.Trade Review“The book contains little theory and presents mostly detailed numerical experiments, it reads very engagingly and inspires with many ideas. It is certainly not a reference book but rather a short monograph on a very clearly defined topic. It will be interesting to see whether the trading strategies presented can be transferred from the crypto markets to the presumably more efficient standard stock markets … as published strategies tend to make markets more efficient.” (Volker H. Schulz, SIAM Review, Vol. 64 (3), September, 2022)Table of ContentsChapter 1 - Introduction Chapter 2 - Related work Chapter 3 - Implementation Chapter 4 - Results Chapter 5 - Conclusions and future work

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Book SynopsisThis volume includes contributions from the 9th Parallel-in-Time (PinT) workshop, an annual gathering devoted to the field of time-parallel methods, aiming to adapt existing computer models to next-generation machines by adding a new dimension of scalability. As the latest supercomputers advance in microprocessing ability, they require new mathematical algorithms in order to fully realize their potential for complex systems. The use of parallel-in-time methods will provide dramatically faster simulations in many important areas, including biomedical (e.g., heart modeling), computational fluid dynamics (e.g., aerodynamics and weather prediction), and machine learning applications. Computational and applied mathematics is crucial to this progress, as it requires advanced methodologies from the theory of partial differential equations in a functional analytic setting, numerical discretization and integration, convergence analyses of iterative methods, and the development and implementation of new parallel algorithms. Therefore, the workshop seeks to bring together an interdisciplinary group of experts across these fields to disseminate cutting-edge research and facilitate discussions on parallel time integration methods. Table of ContentsTight two-level convergence of linear Parareal and MGRIT: Extensions and implications in practice (Southworth et al.).- A Parallel algorithm for solving linear parabolic evolution equations (van Venetië et al.).- Using performance analysis tools for a parallel-in-time integrator (Speck et al.).- Twelve Ways to Fool the Masses When Giving Parallel-In-Time Results (Götschel et al.).- IMEX Runge-Kutta Parareal for Non-Diffusive Equations (Buvoli et al.).

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Book SynopsisThis graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization. Table of ContentsIntroduction.- Matrix analysis and differentiation.- Matrix manifolds in MDA.- Principal component analysis (PCA).- Factor analysis (FA).- Procrustes analysis (PA).- Linear discriminant analysis (LDA).- Canonical correlation analysis (CCA).- Common principal components (CPC).- Metric multidimensional scaling (MDS) and related methods.- Data analysis on simplexes.

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Book SynopsisThis text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.Trade Review“This book has a large amount of new exercise problems that are uniformly distributed across the text. … this book is a very nice text which will serve well for the undergraduate as well as graduate students and will also become a ready reference for scholars.” (Murli M. Gupta, Mathematical Reviews, April, 2023)“Many of the SIAM Review readership will be interested in NMEPPDE from the standpoint of self-study or classroom education. … NMEPPDE offers the applied mathematics reader nearly a single point of entry to our broad and challenging area. … a bit of open space on the bookshelf could profitably be well filled with a copy of NMEPPDE.” (Robert C. Kirby, SIAM Review, Vol. 65 (1), March, 2023)Table of ContentsFor Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson Equation.- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order.- Grid Generation and A Posteriori Error Estimation.- Iterative Methods for Systems of Linear Equations.- Beyond Coercivity, Consistency and Conformity.- Mixed and Nonconforming Discretization Methods.- The Finite Volume Method.- Discretization Methods for Parabolic Initial Boundary Value Problems.- Discretization Methods for Convection-Dominated Problems.- An Outlook to Nonlinear Partial Differential Equations.- Appendices.

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Book SynopsisThis book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.Table of Contents1.Getting Started: Linear Diffusion.- 2.Mathematical Aspects.- 3.Some Variants.- 4.Linear Elasticity and Hyperelasticity.- 5.Elastodynamics.- 6.Contact and Friction.- 7.Plasticity.- 8.Implementaion Aspects.- References.

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