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A survey and some extensions of T. Chan's preconditioner
Jin X.-Q.1; Wei Y.-M.2,3
Source PublicationLinear Algebra and Its Applications

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.

KeywordBlock Operator Circulant Matrix Point Operator T. Chan's circulanT.precondiT.oner T. Chan's precondiT.oner Toeplitz Matrix
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Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000252172800002
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Cited Times [WOS]:9   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Corresponding AuthorWei Y.-M.
Affiliation1.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 AffilicationUniversity of Macau
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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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