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Optimal preconditioners for functions of matrices
Jin X.-Q.; Zhao Z.; Tam S.-C.
Source PublicationLinear Algebra and Its Applications

The optimal preconditioner (A) of a given matrix A was proposed in 1988 by T. Chan [6]. Since then, it has been proved to be efficient for solving a large class of structured systems. In this paper, we construct the optimal preconditioners for different functions of matrices. More precisely, let f be a function of matrices from Cn× to Cn×. Given A∈Cn×, there are two possible optimal preconditioners for f(A): (f(A)) and f( (A)). In the paper, we study properties of both (f(A)) and f((A)) for different functions of matrices. Numerical experiments are given to illustrate the efficiency of the optimal preconditioners when they are used to solve f(A)x=b. © 2014 Elsevier Inc.

KeywordFunctions Of Matrices Optimal Preconditioners Pcg Method Toeplitz Matrix
URLView the original
Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000340330700014
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Corresponding AuthorZhao Z.
AffiliationDepartment of Mathematics, University of Macau, Macao, PR China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Jin X.-Q.,Zhao Z.,Tam S.-C.. Optimal preconditioners for functions of matrices[J]. Linear Algebra and Its Applications,2014,457:224-243.
APA Jin X.-Q.,Zhao Z.,&Tam S.-C..(2014).Optimal preconditioners for functions of matrices.Linear Algebra and Its Applications,457,224-243.
MLA Jin X.-Q.,et al."Optimal preconditioners for functions of matrices".Linear Algebra and Its Applications 457(2014):224-243.
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