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Some relationships between optimal preconditioner and superoptimal preconditioner
Jian-Biao Chen1; Xiao-Qing Jin1; Yi-Min Wei2; Zhao-Liang Xu1
2010
Source PublicationMatrix Methods: Theory, Algorithms and Applications
Pages266-272
Abstract

For any given n-by-n matrix An, a specific circulant preconditioner tF(An) proposed by E. Tyrtyshnikov [SIAM J. Matrix Anal. Appl., Vol. 13 (1992), pp. 459–473] is defined to be the solution of  over all n-by-n nonsingular circulant matrices Cn. The tF(An), called the superoptimal circulant preconditioner, has been proved to be a good preconditioner for a large class of structured systems including some ill-conditioned problems from image processing. In this paper, we study this preconditioner from an operator viewpoint. We will give some relationships between the optimal preconditioner (operator) proposed by T. Chan [SIAM J. Sci. Statist. Comput., Vol. 9 (1988), pp. 766–771] and superoptimal preconditioner (operator).

DOI10.1142/9789812836021_0017
URLView the original
Language英语
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Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Affiliation1.University of Macau
2.Fudan University
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Jian-Biao Chen,Xiao-Qing Jin,Yi-Min Wei,et al. Some relationships between optimal preconditioner and superoptimal preconditioner[J]. Matrix Methods: Theory, Algorithms and Applications,2010:266-272.
APA Jian-Biao Chen,Xiao-Qing Jin,Yi-Min Wei,&Zhao-Liang Xu.(2010).Some relationships between optimal preconditioner and superoptimal preconditioner.Matrix Methods: Theory, Algorithms and Applications,266-272.
MLA Jian-Biao Chen,et al."Some relationships between optimal preconditioner and superoptimal preconditioner".Matrix Methods: Theory, Algorithms and Applications (2010):266-272.
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