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The Sine Transform Operator in the Banach Space of Symmetric Matrices and Its Application in Image Restoration
Kit-Ian KOU; Xiao-Qing JIN; Vai-Kuong SIN
1999-11
Source PublicationNumerical Mathematics A Journal of Chinese Universities(English Series)
ISSN1004-8979
Volume8Issue:2Pages:231-242
Abstract

In this paper, we study an operator s which maps every n-by-n symmetric matrix An to a matrix s(An) that minimizes ||Bn −An||F over the set of all matrices Bn that can be diagonalized by the sine transform. The matrix s(An), called the optimal sine transform preconditioner, is defined for any n-by-n symmetric matrices An. The cost of constructing s(An) is the same as that of optimal circulant preconditioner c(An) which is defined in [8]. The s(An) has been proved in [6] to be a good preconditioner in solving symmetric Toeplitz systems with the preconditioned conjugate gradient (PCG) method. In this paper, we discuss the algebraic and geometric properties of the operator s, and compute its operator norms in Banach spaces of symmetric matrices. Some numerical tests and an application in image restoration are also given.

KeywordToeplitz Matrix Optimal Sine Transform Preconditioner Sine Transform Operator Pcg Method Image Restoration
URLView the original
Language英语
Fulltext Access
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
AffiliationFaculty of Science and Technology University of Macau, Macau
First Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Kit-Ian KOU,Xiao-Qing JIN,Vai-Kuong SIN. The Sine Transform Operator in the Banach Space of Symmetric Matrices and Its Application in Image Restoration[J]. Numerical Mathematics A Journal of Chinese Universities(English Series),1999,8(2):231-242.
APA Kit-Ian KOU,Xiao-Qing JIN,&Vai-Kuong SIN.(1999).The Sine Transform Operator in the Banach Space of Symmetric Matrices and Its Application in Image Restoration.Numerical Mathematics A Journal of Chinese Universities(English Series),8(2),231-242.
MLA Kit-Ian KOU,et al."The Sine Transform Operator in the Banach Space of Symmetric Matrices and Its Application in Image Restoration".Numerical Mathematics A Journal of Chinese Universities(English Series) 8.2(1999):231-242.
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