UM  > Faculty of Science and Technology
Convergence analysis of superoptimal PCG algorithm for Toeplitz systems with a Fisher–Hartwig singularity
Seak-Weng Vong; Wei Wang; Xiao-Qing Jin
2008-01-15
Source PublicationLinear Algebra and its Applications
ISSN0024-3795
Volume428Issue:2-3Pages:535-549
Abstract

Recently, Lu and Hurvich [Y. Lu, C. Hurvich, On the complexity of the preconditioned conjugate gradient algorithm for solving toeplitz systems with a Fisher–Hartwig singularity, SIAM J. Matrix Anal. Appl. 27 (2005) 638–653] used the preconditioned conjugate gradient method with the optimal circulant preconditioner proposed in Chan [T. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput. 9 (1988) 766–771] for solving the Toeplitz system Tn(f )x = b where the generating function f is given by f (ω) = |1 − e−iω| −2dh(ω) with d ∈ −1 2 , 1 2 \{0}. The function h(ω) is positive continuous on [−π, π] and differentiable on [−π, π]\{0}. In this paper, we will use the superoptimal circulant preconditioner proposed by Tyrtyshnikov [E. Tyrtyshnikov, Optimal and superoptimal circulant preconditioners, SIAM J. Matrix Anal. Appl. 13 (1992) 459–473] to solve the same problem when 0

KeywordPcg Method Superoptimal Circulant Preconditioner Toeplitz System Fisher–hartwig Singularity Optimal Circulant Preconditioner
DOIhttps://doi.org/10.1016/j.laa.2007.05.032
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000252172800011
Fulltext Access
Citation statistics
Cited Times [WOS]:0   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Corresponding AuthorSeak-Weng Vong; Xiao-Qing Jin
AffiliationDepartment of Mathematics, University of Macau, Macao, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Seak-Weng Vong,Wei Wang,Xiao-Qing Jin. Convergence analysis of superoptimal PCG algorithm for Toeplitz systems with a Fisher–Hartwig singularity[J]. Linear Algebra and its Applications,2008,428(2-3):535-549.
APA Seak-Weng Vong,Wei Wang,&Xiao-Qing Jin.(2008).Convergence analysis of superoptimal PCG algorithm for Toeplitz systems with a Fisher–Hartwig singularity.Linear Algebra and its Applications,428(2-3),535-549.
MLA Seak-Weng Vong,et al."Convergence analysis of superoptimal PCG algorithm for Toeplitz systems with a Fisher–Hartwig singularity".Linear Algebra and its Applications 428.2-3(2008):535-549.
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
[Seak-Weng Vong]'s Articles
[Wei Wang]'s Articles
[Xiao-Qing Jin]'s Articles
Baidu academic
Similar articles in Baidu academic
[Seak-Weng Vong]'s Articles
[Wei Wang]'s Articles
[Xiao-Qing Jin]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Seak-Weng Vong]'s Articles
[Wei Wang]'s Articles
[Xiao-Qing Jin]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.