Language: English
ISBN/ISSN: 7030107195
Published on: 2006-01
Paperback
This volume contains the latest developments in the use of iterative methods to block Toeplitz systems. These systems arise in a variety of applications in mathematics, scientific computing and engineering, such as image processing, numerical differential equations and integral equations, time series analysis and control theory. Iterative methods such as Krylov subspace methods and multigrid methods are proposed to solve block Teoplitz systems. One of the main advantages of these iterative methods is that the operation cost of solving a large class of mnxmn block Toeplitz systems only requires O(mn log mn)operations.
This book is the first on Toeplitz iterative solvers and it includes recent research results. The author belongs to one of the most important groups in the field of structured matrix computation. The book is accessible to readers with a working knowledge of numerical linear algebra. It should be of interest to everyone who deals with block Toeplitz systems, numerical linear algebra, partial differential equations, ordinary differential equations, image processing and approximation theory.
CONTENTS
Preface
Chapter 1 Introduction
Chapter 2 Block Circulant Preconditioners
Chapter 3 BCCB Preconditioners from Kernels
Chapter 4 Fast Algorthm for Tensor Structure
Chapter 5 Block Toeplitz LS Problems
Chapter 6 Block {w}-Circulant Preconditoners
Chapter 7 Non-Circulant Block Preconditioners
Chapter 8 Multigrid Block Toeplitz Solvers
Chapter 9 Applications in Second-Order PDEs
Chapter 10 Applications in First-Order PDEs
Chapter 11 Applications in ODEs and DAEs
Chapter 12 Applications in Image Processign
Bibliography
Index
