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Some relationships between optimal preconditioner and superoptimal preconditioner
Chen J.B.3; Xu Z.L.3; Jin X.Q.2; Wei Y.M.1
2010
AbstractFor any given n-by-n matrix A, a specific circulant preconditioner tp (An] proposed by B. 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 C- The tF (A), 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).
KeywordOptimal preconditioner Superoptimal preconditioner
ISBN9789812836021;9812836012;9789812836014;
DOI10.1142/9789812836021_0015
URLView the original
Pages266-272
Language英語
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Document TypeBook
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Fudan University
2.Universidade de Macau
3.Shanghai Maritime University
Recommended Citation
GB/T 7714
Chen J.B.,Xu Z.L.,Jin X.Q.,et al. Some relationships between optimal preconditioner and superoptimal preconditioner[M],2010.
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