Description
Book SynopsisThis second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of the two new chapters are integral equations and mathematical optimization. The book provides alternative solutions to software tools amenable to hand computations to validate the results obtained by black box solvers. It also offers an insight into the mathematics behind many CAD, CAE tools of the industry. The book aims to provide a working knowledge of the various approximation techniques for engineering practice.
Trade Review"Dr. Komzsik's book is a rare combination of the basic knowledge in the areas of approximation and computational mechanics which is essential for an engineer. Exhaustive coverage of all the topics along with lucid presentation of the concepts and a wide variety of illustrative problems make this book a valuable source for advanced users. Logical sequence of the topics and nomenclature even allows beginners to cope with the complex field of approximation methods in science and technology. This book contains a large amount of information not found in standard textbooks. Written for the engineer involved in complex issues, it combines the modern mathematical standards of numerical analysis with an understanding on how to effectively use these abstract methods.
The new edition features integral equations and mathematical optimization methods toward their practical usage in the focus of finite and boundary element methods in solitary and coupled formulation as well."
—Thomas Flöck, R&D Engineer, Siemens Digital Factory/Motion Control, Erlangen, Germany
"The first edition of Louis Komzsik' s book was an extremely valuable source of numerical routines for the last decade pushing the envelope in automotive applications. We awaited this second edition book for years and looking forward utilizing it in our work.
The BMW i8 model in the picture on the front depicts the various stages of approximations during the development of a car, ranging from sketches through finite element models to the final geometry. In this process engineers use many of the methods described in this book."
—Daniel Heiserer, BMW, Munich, Germany
"This book features an approachable blend of theoretical motivation with illustrative examples. Many of the methods described lend themselves to a matrix formulation, making them suitable for implementation using MATLAB®. The second edition is further improved by the inclusion of solution
Table of ContentsPreface. Part I Data approximations. Classical interpolation methods. Approximation with splines. Least squares approximation. Approximation of functions. Numerical differentiation. Numerical integration. Part II Approximate solutions. Nonlinear equations in one variable. Systems of nonlinear equations. Iterative solution of linear systems. Approximate solution of eigenvalue problems. Initial value problems. Boundary value problems. Integral equations. Mathematical optimization.
