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The generalized superoptimal preconditioner
Chen J.-L.1; Jin X.-Q.2
Source PublicationLinear Algebra and Its Applications

For any given n-by-n matrix A, a specific circulant preconditioner t (A) introduced by Tyrtyshnikov [E. Tyrtyshnikov, Optimal and super-optimal circulant preconditioners, SIAM J. Matrix Anal. Appl. 13 (1992) 459-473] is defined to be the solution ofunder(min, C) {norm of matrix} I - C A {norm of matrix}over all n-by-n nonsingular circulant matrices C. The preconditioner t (A), called the superoptimal circulant preconditioner, has been proved to be a good preconditioner for a large class of structured systems. In this paper, we study this preconditioner in the general case by using the Moore-Penrose inverse. We give a formula for the superoptimal preconditioner and discuss the stability properties of this preconditioner. A spectral relation between the optimal and superoptimal preconditioned matrices in the general case is also given. Crown 

KeywordMoore-penrose Inverse Optimal Preconditioner Semi-stablity Spectral Relation Superoptimal Preconditioner
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Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000272954400018
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Corresponding AuthorChen J.-L.
Affiliation1.Department of Mathematics, Southeast University, Nanjing 210096, PR China
2.Department of Mathematics, University of Macau, Macao, PR China
Recommended Citation
GB/T 7714
Chen J.-L.,Jin X.-Q.. The generalized superoptimal preconditioner[J]. Linear Algebra and Its Applications,2010,432(1):203-217.
APA Chen J.-L.,&Jin X.-Q..(2010).The generalized superoptimal preconditioner.Linear Algebra and Its Applications,432(1),203-217.
MLA Chen J.-L.,et al."The generalized superoptimal preconditioner".Linear Algebra and Its Applications 432.1(2010):203-217.
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