Generalization of Strang's preconditioner with applications to Toeplitz least squares problems
Publication in refereed journal

香港中文大學研究人員

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摘要In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices A(n). The n/2th column of our circulant preconditioned S-n is equal to the [n/2]th column of the given matrix A(n). Thus if A(n) is a square Toeplitz matrix, then S-n is just the Strang circulant preconditioner. When S-n is not Hermitian, our circulant preconditioner can be defined as (S-n*S-n)(1/2). This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix A(n) has decaying coefficients away from the main diagonal, then (S-n*S-n)(1/2) is a good preconditioner for A(n). Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min \\b - Ax\\(2). Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.
著者Chan RH, Ng MK, Plemmons RJ
期刊名稱Numerical Linear Algebra with Applications
出版年份1996
月份1
日期1
卷號3
期次1
出版社JOHN WILEY & SONS LTD
頁次45 - 64
國際標準期刊號1070-5325
語言英式英語
關鍵詞atmospheric imaging; circulant preconditioned conjugate gradient method; deconvolution; image restoration; medical imaging; Toeplitz least squares problems
Web of Science 學科類別Mathematics; MATHEMATICS; Mathematics, Applied; MATHEMATICS, APPLIED

上次更新時間 2020-29-11 於 00:28