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 <IT>Ax = b</IT> 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.

Contents

Introduction. 1. Preliminaries. 2. Biorthogonality. 3. Projection Methods for Linear Systems. 4. Lanczos-Type Methods. 5. Hybrid Procedures. 6. Semi-Iterative Methods. 7. Around Richardson's Projection. 8. System of Nonlinear Equations. Appendix. Schur's complement. Sylvester's and Schweins' identities. Bibliography. Index.

Bibliography

Includes bibliographical references (pages 341-390) and index.