Optimal preconditioners for functions of matrices | |
Jin X.-Q.; Zhao Z.; Tam S.-C. | |
2014-09-15 | |
Source Publication | Linear Algebra and Its Applications |
ISSN | 00243795 |
Volume | 457Pages:224-243 |
Abstract | 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. |
Keyword | Functions Of Matrices Optimal Preconditioners Pcg Method Toeplitz Matrix |
DOI | https://doi.org/10.1016/j.laa.2014.05.023 |
URL | View the original |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000340330700014 |
Publisher | ELSEVIER SCIENCE INC |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Zhao Z. |
Affiliation | Department of Mathematics, University of Macau, Macao, PR China |
First Author Affilication | University of Macau |
Corresponding Author Affilication | University 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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