Iterative Methods for Linear and Nonlinear Equations

This book focuses on a small number of methods and treats them in depth.

C. T. Kelley (Author)

9780898713527, Society for Industrial and Applied Mathematics

Paperback / softback, published 1 January 1987

180 pages
25.3 x 17.7 x 0.9 cm, 0.337 kg

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.

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.

Subject Areas: Nonlinear science [PBWR], Optimization [PBU], Numerical analysis [PBKS]