Article ID Journal Published Year Pages File Type
4603092 Linear Algebra and its Applications 2008 10 Pages PDF
Abstract

For any given n-by-n matrix An, T. Chan’s circulant preconditioner cF(An) proposed by T. Chan [T. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput. 9 (1988) 766–771] is defined to be the solution ofminCnAn-Cn‖Fover all n-by-n circulant matrices Cn. The cF(An), called the optimal circulant preconditioner by T. Chan, has been proved to be a good preconditioner for a large class of structured systems. A generalization of T. Chan’s circulant preconditioner was given by Huckle [T. Huckle, Circulant and skew circulant matrices for solving Toeplitz matrix problems, SIAM J. Matrix Anal. Appl. 13 (1992) 767–777] which can be used for solving some general linear systems. In this paper, we review some old and develop some new properties of T. Chan’s circulant preconditioner.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, ,