Iterative Methods For Toeplitz Systems

Hardcover | October 14, 2004

byMichael K. Ng

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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 andtheir 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 thetheory 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 imageprocessing, 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 analyse new methods for othertypes of problems and applications.

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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 andtheir convergence theories. A basic knowledge of...

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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Format:HardcoverDimensions:364 pages, 9.21 × 6.14 × 0.96 inPublished:October 14, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198504209

ISBN - 13:9780198504207

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Table of Contents

1. Notations and definitions2. Iterative methodsTheory3. Toeplitz systems4. Circulant preconditioners5. Non-circulant type preconditioners6. Ill-conditioned Toeplitz systems7. Structured systemsApplications8. Applications to ordinary and partial differential equations9. Applications to queuing networks10. Applications to signal processing11. Applications to image processing12. Applications to integral equations