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Block preconditioners with circulant blocks for general linear systems
Jin X.-Q.1; Lin F.-R.2
Source PublicationComputers and Mathematics with Applications

Block preconditioner with circulant blocks (BPCB) has been used for solving linear systems with block Toeplitz structure since 1992 [R. Chan, X. Jin, A family of block preconditioners for block systems, SIAM J. Sci. Statist. Comput. (13) (1992) 1218-1235]. In this new paper, we use BPCBs to general linear systems (with no block structure usually). The BPCBs are constructed by partitioning a general matrix into a block matrix with blocks of the same size and then applying T. Chan's optimal circulant preconditioner [T. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput. (9) (1988) 766-771] to each block. These BPCBs can be viewed as a generalization of T. Chan's preconditioner. It is well-known that the optimal circulant preconditioner works well for solving some structured systems such as Toeplitz systems by using the preconditioned conjugate gradient (PCG) method, but it is usually not efficient for solving general linear systems. Unlike T. Chan's preconditioner, BPCBs used here are efficient for solving some general linear systems by the PCG method. Several basic properties of BPCBs are studied. The relations of the block partition with the cost per iteration and the convergence rate of the PCG method are discussed. Numerical tests are given to compare the cost of the PCG method with different BPCBs. © 2009 Elsevier Ltd. All rights reserved.

KeywordBpcb Circulant Matrix Optimal Circulant Preconditioner Pcg Method Stability
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Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000270116400003
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Document TypeJournal article
Corresponding AuthorLin F.-R.
Affiliation1.Department of Mathematics, University of Macau, Macao, China
2.Department of Mathematics, Shantou University, Shantou 515063, Guangdong, China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Jin X.-Q.,Lin F.-R.. Block preconditioners with circulant blocks for general linear systems[J]. Computers and Mathematics with Applications,2009,58(7):1309-1319.
APA Jin X.-Q.,&Lin F.-R..(2009).Block preconditioners with circulant blocks for general linear systems.Computers and Mathematics with Applications,58(7),1309-1319.
MLA Jin X.-Q.,et al."Block preconditioners with circulant blocks for general linear systems".Computers and Mathematics with Applications 58.7(2009):1309-1319.
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