A survey and some extensions of T. Chan's preconditioner | |
Jin X.-Q.1; Wei Y.-M.2,3 | |
2008-01-15 | |
Source Publication | Linear Algebra and Its Applications |
ISSN | 00243795 |
Volume | 428Issue:2-3Pages:403-412 |
Abstract | For any given n-by-n matrix A, T. Chan's circulant preconditioner c(A) 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 ofunder(min, C) A - C {norm of matrix}over all n-by-n circulant matrices C. The c(A), 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. © 2007 Elsevier Inc. All rights reserved. |
Keyword | Block Operator Circulant Matrix Point Operator T. Chan's circulanT.precondiT.oner T. Chan's precondiT.oner Toeplitz Matrix |
DOI | https://doi.org/10.1016/j.laa.2007.01.021 |
URL | View the original |
Indexed By | SCIE |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000252172800002 |
Publisher | ELSEVIER SCIENCE INC |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Wei Y.-M. |
Affiliation | 1.Department of Mathematics, University of Macau, Macao, China 2.Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China 3.Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, China |
First Author Affilication | University of Macau |
Recommended Citation GB/T 7714 | Jin X.-Q.,Wei Y.-M.. A survey and some extensions of T. Chan's preconditioner[J]. Linear Algebra and Its Applications,2008,428(2-3):403-412. |
APA | Jin X.-Q.,&Wei Y.-M..(2008).A survey and some extensions of T. Chan's preconditioner.Linear Algebra and Its Applications,428(2-3),403-412. |
MLA | Jin X.-Q.,et al."A survey and some extensions of T. Chan's preconditioner".Linear Algebra and Its Applications 428.2-3(2008):403-412. |
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