Developments and Applications of Block Toeplitz Iterative Solvers

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 Toeplitz systems. One of the main advantages of these iterative methods is that the operation cost of solving a large class of mn × mn block Toeplitz systems only requires O (mn log mn) operations. This book is the first book 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.

Preface. 1. Introduction. 2. Block Circulant Preconditioners. 3. BCCB Preconditioners from Kernels. 4. Fast Algorithm for Tensor Structure. 5. Block Toeplitz LS Problems. 6. Block {omega}-Circulant Preconditioners. 7. Non-Circulant Block Preconditioners. 8. Multigrid Block Toeplitz Solvers. 9. Applications in Second-Order PDEs. 10. Applications in First-Order PDEs. 11. Applications in ODEs and DAEs. 12. Applications in Image Processing. Bibliography. Index.