Author : Society for Industrial and Applied Mathematics
Publisher :
Page : 944 pages
File Size : 19,32 MB
Release : 2005
Category : Numerical analysis
ISBN :
Author : David Gottlieb
Publisher : SIAM
Page : 167 pages
File Size : 14,92 MB
Release : 1977-01-01
Category : Technology & Engineering
ISBN : 0898710235
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Author :
Publisher :
Page : 764 pages
File Size : 10,56 MB
Release : 1964
Category : Electronic journals
ISBN :
Contains research articles on the development and analysis of numerical methods, including their convergence, stability, and error analysis as well as related results in functional analysis and approximation theory. Computational experiments and new types of numerical applications are also included.
Author : Ake Bjorck
Publisher : SIAM
Page : 425 pages
File Size : 44,70 MB
Release : 1996-01-01
Category : Mathematics
ISBN : 9781611971484
The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
Author : Brian Sutton
Publisher : SIAM
Page : 448 pages
File Size : 49,95 MB
Release : 2019-04-18
Category : Mathematics
ISBN : 1611975700
This 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.
Author : Society for Industrial and Applied Mathematics
Publisher :
Page : 1182 pages
File Size : 46,64 MB
Release : 1966
Category : Electronic journals
ISBN :
Author : James W. Demmel
Publisher : SIAM
Page : 426 pages
File Size : 25,53 MB
Release : 1997-08-01
Category : Mathematics
ISBN : 0898713897
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Author : Robert M. Corless
Publisher : Springer Science & Business Media
Page : 896 pages
File Size : 12,72 MB
Release : 2013-12-12
Category : Mathematics
ISBN : 1461484537
This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.
Author : J. E. Dennis, Jr.
Publisher : SIAM
Page : 394 pages
File Size : 29,9 MB
Release : 1996-12-01
Category : Mathematics
ISBN : 9781611971200
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author : Willy J. F. Govaerts
Publisher : SIAM
Page : 384 pages
File Size : 31,99 MB
Release : 2000-01-01
Category : Mathematics
ISBN : 9780898719543
Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.
