Projection Methods for Systems of Equations

Claude Brezinski (Eds.)0444827773, 9780585474298, 9780444827777

The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms.
The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are described which are based on projections. Recently, such methods have received much attention from researchers in numerical linear algebra and have been applied to a wide range of problems.
The book is intended for students and researchers in numerical analysis and for practitioners and engineers who require the most recent methods for solving their particular problem.

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Table of contents :
Content:
Introduction
Pages 1-15

Chapter 1 Preliminaries Original Research Article
Pages 17-59

Chapter 2 Biorthogonality Original Research Article
Pages 61-92

Chapter 3 Projection methods for linear systems Original Research Article
Pages 93-139

Chapter 4 Lanczos-type methods Original Research Article
Pages 141-182

Chapter 5 Hybrid procedures Original Research Article
Pages 183-221

Chapter 6 Semi-iterative methods Original Research Article
Pages 223-245

Chapter 7 Around richardson’s projection Original Research Article
Pages 247-286

Chapter 8 Systems of nonlinear equations Original Research Article
Pages 287-336

Appendix
Pages 337-339

Biblography
Pages 341-390

Index
Pages 391-400