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Superoptimal preconditioners for functions of matrices
Bai Z.-J.1; Jin X.-Q.2; Yao T.-T.1
Source PublicationNumerical Mathematics
ISSN20797338 10048979

For any given matrix A ∈ C, a preconditioner t(A) called the superoptimal preconditioner was proposed in 1992 by Tyrtyshnikov. It has been shown that t(A) is an efficient preconditioner for solving various structured systems, for instance, Toeplitz-like systems. In this paper, we construct the superoptimal preconditioners for different functions of matrices. Let f be a function of matrices from C to C. For any A ∈ C, one may construct two superoptimal preconditioners for f(A): t(f(A)) and f(t(A)). We establish basic properties of t(f(A)) and f(t(A)) for different functions of matrices. Some numerical tests demonstrate that the proposed preconditioners are very efficient for solving the system f(A)x = b.

KeywordFunctions Of Matrices Pcg Method Superoptimal Preconditioners Toeplitz Matrix
URLView the original
WOS Research AreaSuperoptimal Preconditioners For Functions Of Matrices
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000365268800004
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Affiliation1.Xiamen University
2.Universidade de Macau
Recommended Citation
GB/T 7714
Bai Z.-J.,Jin X.-Q.,Yao T.-T.. Superoptimal preconditioners for functions of matrices[J]. Numerical Mathematics,2015,8(4):515-529.
APA Bai Z.-J.,Jin X.-Q.,&Yao T.-T..(2015).Superoptimal preconditioners for functions of matrices.Numerical Mathematics,8(4),515-529.
MLA Bai Z.-J.,et al."Superoptimal preconditioners for functions of matrices".Numerical Mathematics 8.4(2015):515-529.
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