Iterative Methods for Toeplitz Systems

Iterative Methods for Toeplitz Systems

by Michael K. Ng
     
 

ISBN-10: 0198504209

ISBN-13: 9780198504207

Pub. Date: 01/01/2005

Publisher: Oxford University Press, USA

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

…  See more details below

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.

Read More

Product Details

ISBN-13:
9780198504207
Publisher:
Oxford University Press, USA
Publication date:
01/01/2005
Series:
Numerical Mathematics and Scientific Computation Series
Edition description:
New Edition
Pages:
366
Product dimensions:
9.30(w) x 6.20(h) x 1.00(d)

Table of Contents

1Notations and definitions3
2Iterative methods12
3Toeplitz systems25
4Circulant preconditioners48
5Non-circulant type preconditioners80
6Ill-conditioned Toeplitz systems94
7Structured systems134
8Applications to ODEs and PDEs179
9Applications to queueing networks211
10Applications to signal processing238
11Applications to image processing250
12Applications to integral equations285

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >