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An Introduction to Iterative Toeplitz SolversAn Introduction to Iterative Toeplitz Solvers

Raymond Hon-Fu Chan and Xiao-Qing Jin

Toeplitz systems arise in a variety of applications in mathematics, scientific computing, and engineering, including numerical partial and ordinary differential equations, numerical solutions of convolution-type integral equations, stationary autoregressive time series in statistics, minimal realization problems in control theory, system identification problems in signal processing, and image restoration problems in image processing.

This practical book introduces current developments in using iterative methods for solving Toeplitz systems based on the preconditioned conjugate gradient method. The authors focus on the important aspects of iterative Toeplitz solvers and give special attention to the construction of efficient circulant preconditioners. Applications of iterative Toeplitz solvers to practical problems are addressed, enabling readers to use the book’s methods and algorithms to solve their own problems.

An appendix containing the MATLAB® programs used to generate the numerical results is included.

Students and researchers in computational mathematics and scientific computing will benefit from this book.

Iterative method, conjugate gradient method, Toeplitz system, circulant preconditioner, block-Toeplitz system

Table of Contents

Raymond Hon-Fu Chan is a Professor of Mathematics in the Department of Mathematics at the Chinese University of Hong Kong, China.

Xiao-Qing Jin is a Professor in the Department of Mathematics at the University of Macau, China.

2007 / xii + 108 pages / Softcover / ISBN 978-0-898716-36-8
List Price $71.50 / SIAM Member Price $50.05 / Order Code FA05
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