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Iterative Methods for Toeplitz Systems

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Overview

Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed. The first part of the book (chapters one and two) gives a brief review of some terms and results in linear algebra and the conjugate gradient method, which are important topics for handling the mathematics later on in the book. The second part of the book (chapters three to seven) presents the theory of using iterative methods for solving Toeplitz and Toeplitz-related systems. The third part of the book (chapters eight to twelve) presents recent results from applying the use of iterative methods in different fields of applications, such as partial differential equations, signal and image processing, integral equations and queuing networks. These chapters provide research and application-oriented readers with a thorough understanding of using iterative methods, enabling them not only to apply these methods to the problems discussed but also to derive and analyze new methods for other types of problems and applications.

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Product Details

Meet the Author

Michael K. Ng is an Associate Professor in the Department of Mathematics and also Adjunct Research Fellow in the E-Business Technology Institute at The University of Hong Kong.

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Table of Contents

1 Notations and definitions 3
2 Iterative methods 12
3 Toeplitz systems 25
4 Circulant preconditioners 48
5 Non-circulant type preconditioners 80
6 Ill-conditioned Toeplitz systems 94
7 Structured systems 134
8 Applications to ODEs and PDEs 179
9 Applications to queueing networks 211
10 Applications to signal processing 238
11 Applications to image processing 250
12 Applications to integral equations 285
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