Search results for ""Society for Industrial Applied Mathematics,U.S.""
Society for Industrial & Applied Mathematics,U.S. Sparse Solutions of Underdetermined Linear Systems
This textbook presents a special solution of underdetermined linear systems where the number of nonzero entries in the solution is very small compared to the total number of entries. This is called sparse solution. As underdetermined linear systems can be very different, the authors explain how to compute a sparse solution by many approaches.Sparse Solutions of Underdetermined Linear Systems: Contains 72 algorithms for finding sparse solutions of underdetermined linear systems and their applications for matrix completion, graph clustering, and phase retrieval. Provides a detailed explanation of these algorithms including derivations and convergence analysis. Includes exercises for each chapter to help the reader understand the material. This textbook is appropriate for graduate students in math and applied math, computer science, statistics, data science, and engineering. Advisors and postdocs will also find the book of interest.It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.
£100.12
Society for Industrial & Applied Mathematics,U.S. Mathematics and Tools for Financial Engineering
Based on a master's program course at the University of Southern California, the main goal of Mathematics and Tools for Financial Engineering is to train students to use mathematical and engineering tools to understand and solve financial problems. The book contains numerous examples and problems and is divided into two parts: Part I covers mathematical preliminaries (set theory, linear algebra, sequences and series, real functions and analysis, numerical approximations and computations, basic optimization theory, and stochastic processes). Part II addresses financial topics, ranging from low- to high-risk investments. Mathematics and Tools for Financial Engineering is intended for senior undergraduate or graduate students in finance or financial engineering. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Readers with no prior knowledge in finance can use the book to learn about various mathematical theories and tools.
£85.17
Society for Industrial & Applied Mathematics,U.S. Interpolatory Methods for Model Reduction
Dynamical 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.
£84.17
Society for Industrial & Applied Mathematics,U.S. Computed Tomography: Algorithms, Insight, and Just Enough Theory
In Computed Tomography: Algorithms, Insight, and Just Enough Theory, readers will learn about the fundamental computational methods used for image reconstruction in computed tomography (CT). Unique in its emphasis on the interplay of modeling, computing, and algorithm development, the book presents underlying mathematical models for motivating and deriving the basic principles of CT reconstruction methods, along with insight into their advantages, limitations, and computational aspects.Computed Tomography: Algorithms, Insight, and Just Enough Theory: Develops the mathematical and computational aspects of three main classes of reconstruction methods. Emphasizes the link between CT and numerical methods, which is rarely found in current literature. Describes the effects of incomplete data using both microlocal analysis and the singular value decomposition (SVD). Contains computer exercises using MATLAB that allow readers to experiment with the algorithms and make the book suitable for teaching and self-study. This book is aimed at students, researchers, and practitioners. As a textbook, it is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.
£92.15
Society for Industrial & Applied Mathematics,U.S. Sparse Polynomial Approximation of High-Dimensional Functions
Over 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.
£95.14
Society for Industrial & Applied Mathematics,U.S. Matrix Analysis and Computations
Matrix Analysis and Computations introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations. In this textbook, readers will find: The matrix theory necessary for direct and iterative methods for solving systems of linear equations. Systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods. Current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. Exercises at the end of each chapter for applying learned methods. This book is intended for graduate students, researchers, and engineers interested in matrix analysis and matrix computations. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.
£101.12
Society for Industrial & Applied Mathematics,U.S. Numerical Linear Algebra with Julia
Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. The style is friendly and approachable and cartoon characters guide the way.Inside this book, readers will find detailed descriptions of algorithms, implementations in Julia that illustrate concepts and allow readers to explore methods on their own, and illustrations and graphics that emphasize core concepts and demonstrate algorithms. Numerical Linear Algebra with Julia is a textbook for undergraduate and graduate students. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. The book may also serve as a reference for researchers in various fields such as computational engineering, statistics, data-science, and machine learning, who depend on numerical solvers in linear algebra.
£95.14
Society for Industrial & Applied Mathematics,U.S. Complex Variables and Analytic Functions: An Illustrated Introduction
At almost all academic institutions worldwide, complex variables and analytic functions are utilized in courses on applied mathematics, physics, engineering, and other related subjects. For most students, formulas alone do not provide a sufficient introduction to this widely taught material, yet illustrations of functions are sparse in current books on the topic. This is the first primary introductory textbook on complex variables and analytic functions to make extensive use of functional illustrations. Aiming to reach undergraduate students entering the world of complex variables and analytic functions, this book utilizes graphics to visually build on familiar cases and illustrate how these same functions extend beyond the real axis. It covers several important topics that are omitted in nearly all recent texts, including techniques for analytic continuation and discussions of elliptic functions and of Wiener–Hopf methods. It also presents current advances in research, highlighting the subject’s active and fascinating frontier.The primary audience for this textbook is undergraduate students taking an introductory course on complex variables and analytic functions. It is also geared toward graduate students taking a second semester course on these topics, engineers and physicists who use complex variables in their work, and students and researchers at any level who want a reference book on the subject.
£95.14
Society for Industrial & Applied Mathematics,U.S. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems
Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements.The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications.Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.
£100.12
Society for Industrial & Applied Mathematics,U.S. An Introduction to the Numerical Simulation of Stochastic Differential Equations
This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous computational examples and computer code is listed at the end of each chapter. The authors include 150 exercises, with solutions available online, and 40 programming tasks.Although introductory, the book covers a range of modern research topics, including Itô versus Stratonovich calculus, implicit methods, stability theory, nonconvergence on nonlinear problems, multilevel Monte Carlo, approximation of double stochastic integrals, and tau leaping for chemical and biochemical reaction networks.An Introduction to the Numerical Simulation of Stochastic Differential Equations is appropriate for undergraduates and postgraduates in mathematics, engineering, physics, chemistry, finance, and related disciplines, as well as researchers in these areas. The material assumes only a competence in algebra and calculus at the level reached by a typical first-year undergraduate mathematics class, and prerequisites are kept to a minimum. Some familiarity with basic concepts from numerical analysis and probability is also desirable but not necessary.
£89.16
Society for Industrial & Applied Mathematics,U.S. Practical Methods for Optimal Control Using Nonlinear Programming
How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these.This third edition focuses on the direct transcription method for optimal control, and features: A summary of relevant material in constrained optimization, including nonlinear programming. Discretization techniques appropriate for ordinary differential equations and differential-algebraic equations. Several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes: New material on implicit Runge–Kutta discretization techniques. New chapters on partial differential equations and delay equations. More than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.
£133.03
Society for Industrial & Applied Mathematics,U.S. Mastering Frequency Domain Techniques for the Stability Analysis of LTI Time Delay Systems
In many dynamical systems, time delays arise because of the time it takes to measure system states, perceive and evaluate events, formulate decisions, and act on those decisions. The presence of delays may lead to undesirable outcomes; without an engineered design, the dynamics may underperform, oscillate, and even become unstable. How to study the stability of dynamical systems influenced by time delays is a fundamental question. Related issues include how much time delay the system can withstand without becoming unstable and how to change system parameters to render improved dynamic characteristics, utilize or tune the delay itself to improve dynamical behavior, and assess the stability and speed of response of the dynamics. Mastering Frequency Domain Techniques for the Stability Analysis of LTI Time Delay Systems addresses these questions for linear time-invariant (LTI) systems with an eigenvalue-based approach built upon frequency domain techniques. Readers will find key results from the literature, including all subtopics for those interested in deeper exploration. The book presents step-by-step demonstrations of all implementations—including those that require special care in mathematics and numerical implementation—from the simpler, more intuitive ones in the introductory chapters to the more complex ones found in the later chapters. Maple and MATLAB code is available from the author’s website.This multipurpose book is intended for graduate students, instructors, and researchers working in control engineering, robotics, mechatronics, network control systems, human-in-the-loop systems, human-machine systems, remote control and tele-operation, transportation systems, energy systems, and process control, as well as for those working in applied mathematics, systems biology, and physics. It can be used as a primary text in courses on stability and control of time delay systems and as a supplementary text in courses in the above listed domains.
£84.17
Society for Industrial & Applied Mathematics,U.S. Nonlocal Modeling, Analysis, and Computation
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas.Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics.A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to traditional local systems represented by partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives to as well as bridges to existing local continuum and discrete models.The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on existing discrete models and local continuum models and the connections between them.
£64.22
Society for Industrial & Applied Mathematics,U.S. An Introduction to Singular Integrals
In just over 100 pages, this book provides basic, essential knowledge of some of the tools of real analysis: the Hardy–Littlewood maximal operator, the Calderón–Zygmund theory, the Littlewood–Paley theory, interpolation of spaces and operators, and the basics of H1 and BMO spaces. This concise text offers brief proofs and exercises of various difficulties designed to challenge and engage students. An Introduction to Singular Integrals is meant to give first-year graduate students in Fourier analysis and partial differential equations an introduction to harmonic analysis. While some background material is included in the appendices, readers should have a basic knowledge of functional analysis, some acquaintance with measure and integration theory, and familiarity with the Fourier transform in Euclidean spaces.
£66.21