Iterative Methods for Toeplitz Systems by Michael K. Ng (English) Hardcover Book

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Iterative Methods for Toeplitz Systems by Michael K. Ng

Deals 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.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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 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. Thesecond 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 thoroughunderstanding 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 other types of problems and applications.

Table of Contents

1: Notations and definitions 2: Iterative methods Theory 3: Toeplitz systems 4: Circulant preconditioners 5: Non-circulant type preconditioners 6: Ill-conditioned Toeplitz systems 7: Structured systems Applications 8: Applications to ordinary and partial differential equations 9: Applications to queuing networks 10: Applications to signal processing 11: Applications to image processing 12: Applications to integral equations

Review

The book gives an excellent overview of the research and results in this area during the last few decades. * EMS Newsletter *

Long Description

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 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 analyse new methods for other types of problems and applications.

Review Text

1. Notations and definitions 2. Iterative methods Theory 3. Toeplitz systems 4. Circulant preconditioners 5. Non-circulant type preconditioners 6. Ill-conditioned Toeplitz systems 7. Structured systems Applications 8. Applications to ordinary and partial differential equations 9. Applications to queuing networks 10. Applications to signal processing 11. Applications to image processing 12. Applications to integral equations

Review Quote

The book gives an excellent overview of the research and results in this area during the last few decades.

Feature

Broad range of applications in mathematics and engineering
Comprehensive overview of developments over last decade
Provides thorough background for deriving and analysing new methods
Includes many exercises for self-study

Details ISBN0198504209 Author Michael K. Ng Short Title ITERATIVE METHODS FOR TOEPLITZ Language English ISBN-10 0198504209 ISBN-13 9780198504207 Media Book Format Hardcover Year 2004 Imprint Oxford University Press Place of Publication Oxford Country of Publication United Kingdom Affiliation Department of Mathematics, The University of Hong Kong DOI 10.1604/9780198504207 UK Release Date 2004-10-14 NZ Release Date 2004-10-14 Birth 1930 Position Lecturer in Philosophy Qualifications Jr. Pages 368 Publisher Oxford University Press Series Numerical Mathematics and Scientific Computation Publication Date 2004-10-14 DEWEY 515.7246 Illustrations 18 b/w line, 11 halftones Audience Professional & Vocational AU Release Date 2004-11-30 Country of Origin US Product Class Description Engineering & Technology: Textbooks & Study Guides
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