The book gives an excellent overview of the research and results in this area during the last few decades.
EMS Newsletter
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 analyse new methods for other types of problems and applications.
Les mer
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.
Les mer
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
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The book gives an excellent overview of the research and results in this area during the last few decades.
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
Les mer
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.
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
Les mer
Produktdetaljer
ISBN
9780198504207
Publisert
2004
Utgiver
Vendor
Oxford University Press
Vekt
702 gr
Høyde
242 mm
Bredde
163 mm
Dybde
24 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
368
Forfatter