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Preconditioners for ill-conditioned block Toeplitz systems with application in image restoration
Lei S.-L.; Kou K.-I.; Jin X.-Q.
1999-12-01
Source PublicationEast-West Journal of Numerical Mathematics
ISSN09280200
Volume7Issue:3Pages:175-185
Abstract

The convergence rate of the conjugate gradient (CG) method for solving ill-conditioned Toeplitz systems is slow usually. To deal with such kind of systems, Potts and Steidl proposed in [11] an {ωRTBC-circulant preconditioner for solving these systems by using the preconditioned conjugate gradient (PCG) method. It was showed that the convergence rate of the PCG method is superlinear and the total operation cost is O(N log N), where N is the size of the system. Furthermore, it was suggested that the {ωRTBC-circulant preconditioner can also work efficiently for solving block Toeplitz systems. In this paper, we generalize this preconditioner for block systems. Both theoretical and numerical results are given. Besides, we apply this block preconditioner in image restoration.

URLView the original
Language英语
Fulltext Access
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
AffiliationUniversidade de Macau
Recommended Citation
GB/T 7714
Lei S.-L.,Kou K.-I.,Jin X.-Q.. Preconditioners for ill-conditioned block Toeplitz systems with application in image restoration[J]. East-West Journal of Numerical Mathematics,1999,7(3):175-185.
APA Lei S.-L.,Kou K.-I.,&Jin X.-Q..(1999).Preconditioners for ill-conditioned block Toeplitz systems with application in image restoration.East-West Journal of Numerical Mathematics,7(3),175-185.
MLA Lei S.-L.,et al."Preconditioners for ill-conditioned block Toeplitz systems with application in image restoration".East-West Journal of Numerical Mathematics 7.3(1999):175-185.
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