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Iterative Methods for Linear and Nonlinear Equations

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by C. T. Kelley


1995 / xiv + 166 pages/ Softcover/ ISBN: 978-0-898713-52-7 / List Price $66.00 / SIAM Member Price $46.20 / Order Code FR16


Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth.

The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods.

Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.

This book can be used as a tutorial and a reference by anyone who needs to solve nonlinear systems of equations or large linear systems. It may also be used as a textbook for introductory courses in nonlinear equations or iterative methods or as source material for an introductory course in numerical analysis at the graduate level. The reader should be familiar with elementary numerical analysis, linear algebra, and the central ideas of direct methods for the numerical solution of dense linear systems.

Preface; How to Get the Software; Part I: Linear Equations. Chapter 1: Basic Concepts and Stationary Iterative Methods; Chapter 2: Conjugate Gradient Iteration; Chapter 3: GMRES Iteration; Part II: Nonlinear Equations. Chapter 4: Basic Concepts and Fixed Point Iteration; Chapter 5: Newton's Method; Chapter 6: Inexact Newton Methods; Chapter 7: Broyden's Method; Chapter 8: Global Convergence; Bibliography; Index.

ISBN: 9780898713527

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