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Polynomial Based Iteration Methods for Symmetric Linear SystemsPolynomial Based Iteration Methods for Symmetric Linear Systems

Bernd Fischer

Classics in Applied Mathematics 68

This book provides a concise introduction to computational methods for solving large linear systems of equations. It is the only textbook that treats iteration methods for symmetric linear systems from a polynomial point of view. This particular feature enables readers to understand the convergence behavior and subtle differences of the various schemes, which are useful tools for the design of powerful preconditioners.

Published nearly 15 years ago, Polynomial Based Iteration Methods for Symmetric Linear Systems continues to be useful to the mathematical, scientific, and engineering communities as a presentation of what appear to be the most efficient methods for symmetric linear systems of equations.

To help potential users of numerical iteration algorithms design schemes for their particular needs, the author provides MATLAB® code on a supplementary Web page to serve as a guideline. The code not only solves the linear system but also computes the underlying residual polynomials, illustrating the convergence behavior of the given linear system.

This book is appropriate for researchers and advanced undergraduate and graduate students using numerical linear algebra, as well as practitioners working in applications that lead to symmetric indefinite systems.

Preface to the Classics Edition:
Chapter 1- Introduction;
Chapter 2- Orthogonal Polynomials;
Chapter 3- Chebyshev and Optimal Polynomials;
Chapter 4- Orthogonal Polynomials and Krylov Subspaces;
Chapter 5- Estimating the Spectrum and the Distribution Function;
Chapter 6- Parameter Free Methods;
Chapter 7- Parameter Dependent Methods;
Chapter 8- The Stokes Problem;
Chapter 9- Approximating the A-Norm;

About the Author
Bernd Fischer is Professor of Applied Mathematics, Director of the Institute of Mathematics and Image Computing, and head of the Fraunhofer Project Group on Image Registration at the University of Lübeck, Germany. His research interests include the solution of large linear systems of equations, the design and numerical treatment of dynamical systems in medical applications, and mathematical aspects of digital image processing, especially medical image registration problems.

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Symmetric linear systems, polynomial iteration methods, Krylov subspace methods, numerical linear algebra, orthogonal polynomials

2011 / 283 pages / Softcover / ISBN 978-1-611971-91-0
List Price $85.00 / Member Price $59.50 / Order Code CL68
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Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)