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BCCB preconditioners for systems of BVM-based numerical integrators
Lei S.-L.; Jin X.-Q.
2004-06-05
Source PublicationNumerical Linear Algebra with Applications
ISSN10705325
Volume11Issue:1Pages:25-40
Abstract

Boundary value methods (BVMs) for ordinary differential equations require the solution of nonsymmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A block-circulant preconditioner with circulant blocks (BCCB preconditioner) is proposed to speed up the convergence rate of the GMRES method. The BCCB preconditioner is shown to be invertible when the BVM is A -stable. The spectrum of the preconditioned matrix is clustered and therefore, the preconditioned GMRES method converges fast. Moreover, the operation cost in each iteration of the preconditioned GMRES method by using our BCCB preconditioner is less than that required by using block-circulant preconditioners proposed earlier. In numerical experiments, we compare the number of iterations of various preconditioners. 

KeywordBccb Preconditioner Block-circulant Preconditioner Bvm Gmres Method Ode Toeplitz Matrix
DOI10.1002/nla.331
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000188811700002
PublisherWILEY-BLACKWELL
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Citation statistics
Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
AffiliationDepartment of Mathematics, University of Macau, Macau, China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lei S.-L.,Jin X.-Q.. BCCB preconditioners for systems of BVM-based numerical integrators[J]. Numerical Linear Algebra with Applications,2004,11(1):25-40.
APA Lei S.-L.,&Jin X.-Q..(2004).BCCB preconditioners for systems of BVM-based numerical integrators.Numerical Linear Algebra with Applications,11(1),25-40.
MLA Lei S.-L.,et al."BCCB preconditioners for systems of BVM-based numerical integrators".Numerical Linear Algebra with Applications 11.1(2004):25-40.
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