Sine transform based preconditioners for symmetric Toeplitz systems
Publication in refereed journal

香港中文大學研究人員

引用次數
替代計量分析
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其它資訊
摘要The optimal circulant preconditioner for a given matrix A is defined to be the minimizer of \\C-A\\(F) over the set of all circulant matrices C. Here \\.\\(F) is the Frobenius norm. Optimal circulant preconditioners have been proved to be good preconditioners in solving Toeplitz systems with the preconditioned conjugate gradient ent method. In this paper, we construct an optimal sine transform based preconditioner which is defined to be the minimizer of \\B-A\\(F) over the set of matrices B that can be diagonalized by sine transforms. We mill prove that for general n-by-n matrices A, these optimal preconditioners can be constructed in O(n(2)) real operations and in O(n) real operations if A is Toeplitz. We will also show that the convergence properties of these optimal sine transform preconditioners are the same as that of the optimal circulant ones when they are employed to solve Toeplitz systems. Numerical examples are given to support our convergence analysis.
著者Chan RH, Ng MK, Wong CK
期刊名稱Linear Algebra and its Applications
出版年份1996
月份1
日期1
卷號232
出版社ELSEVIER SCIENCE INC
頁次237 - 259
國際標準期刊號0024-3795
語言英式英語
Web of Science 學科類別Mathematics; Mathematics, Applied; MATHEMATICS, APPLIED

上次更新時間 2020-29-11 於 00:25