Iterative methods for linear and nonlinear equations / C.T. Kelley.

Format:

Book

Author/Creator:

Kelley, C. T.

Contributor:

Society for Industrial and Applied Mathematics.

Series:

Frontiers in applied mathematics ; 16.

Frontiers in applied mathematics ; 16

Language:

English

Subjects (All):

Iterative methods (Mathematics).

Physical Description:

1 online resource (xiii, 165 p. ) ill. ;

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1995.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 153-162) and index.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-094-6

Publisher Number:

FR16 SIAM