UM  > 科技學院  > 數學系
 Superoptimal preconditioners for functions of matrices Bai Z.-J.1; Jin X.-Q.2; Yao T.-T.1 2015-11 Source Publication Numerical Mathematics ISSN 20797338 10048979 Volume 8Issue:4Pages:515-529 Abstract 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. Keyword Functions Of Matrices Pcg Method Superoptimal Preconditioners Toeplitz Matrix DOI 10.4208/nmtma.2015.my1340 URL View the original Language 英语 WOS Research Area Superoptimal Preconditioners For Functions Of Matrices WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000365268800004 Publisher CAMBRIDGE UNIV PRESS Fulltext Access Citation statistics Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS] Document Type Journal article Collection DEPARTMENT OF MATHEMATICS Affiliation 1.Xiamen University2.Universidade de Macau Recommended CitationGB/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.
 Files in This Item: There are no files associated with this item.
 Related Services Recommend this item Bookmark Usage statistics Export to Endnote Google Scholar Similar articles in Google Scholar [Bai Z.-J.]'s Articles [Jin X.-Q.]'s Articles [Yao T.-T.]'s Articles Baidu academic Similar articles in Baidu academic [Bai Z.-J.]'s Articles [Jin X.-Q.]'s Articles [Yao T.-T.]'s Articles Bing Scholar Similar articles in Bing Scholar [Bai Z.-J.]'s Articles [Jin X.-Q.]'s Articles [Yao T.-T.]'s Articles Terms of Use No data! Social Bookmark/Share