Iterative Methods for Linear and Nonlinear Equations

C.T. Kelley, H. T. Banks

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English

Society for Industrial & Applied Mathematics,U.S.
31 January 2026

Differential calculus & equations; Maths for scientists; Maths for engineers

Series: Frontiers in Applied Mathematics

This book is devoted to giving a modern view of iterative methods for solving linear and nonlinear equations, which are the basis for many, if not most, of the models of phenomena in science and engineering; their efficient numerical solution is critical to progress in these areas. The text provides motivating examples mainly from boundary value problems with partial differential equations, and many of the chapters contain links to MATLAB code, which is provided per anonymous ftp by the author.

This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, considerable material on linear equations has been incorporated. It 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.

By: C.T. Kelley, H. T. Banks
Imprint: Society for Industrial & Applied Mathematics,U.S.
Country of Publication: United States
Volume: 18
Dimensions: Height: 251mm, Width: 178mm, Spine: 12mm
Weight: 345g
ISBN: 9780898713527
ISBN 10: 0898713528
Series: Frontiers in Applied Mathematics
Pages: 179
Publication Date: 31 January 2026
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Forthcoming

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