CONSTRUCTION OF PRECONDITIONERS FOR WIENER-HOPF EQUATIONS BY OPERATOR SPLITTING
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香港中文大學研究人員

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摘要In this paper, we propose a new type of preconditioners for solving finite section Wiener-Hopf integral equations (alpha I + A(tau))x(tau) = g by the preconditioned conjugate gradient algorithm. We show that for an integer u > 1, the operator alpha I + A(tau) can be decomposed into a sum of operators alpha I + P-tau((u,v)) for 0 less than or equal to v < u. Here P-tau((u,v)) are {omega(v)}-circulant integral operators that are the continuous analog of {omega(v)}-circulant matrices. For u greater than or equal to 1, our preconditioners are defined as (1/u) Sigma(v)(alpha I + P-tau((u,v)))(-1). Thus the way the preconditioners are constructed is very similar to the approach used in the additive Schwarz method for elliptic problems. As for the convergence rate, we prove that the spectra of the resulting preconditioned operators [(1/u) Sigma(v)(alpha I + P-tau((u,v)))(-1)] [alpha I + A(tau)] are clustered around 1 and thus the algorithm converges sufficiently fast. Finally, we discretize the resulting preconditioned equations by rectangular rule. Numerical results show that our methods converges faster than those preconditioned by using circulant integral operators.
著者NG MK, LIN FR, CHAN RH
期刊名稱Applied Mathematics and Computation
出版年份1995
月份9
日期15
卷號72
期次1
出版社ELSEVIER SCIENCE PUBL CO INC
頁次77 - 96
國際標準期刊號0096-3003
電子國際標準期刊號1873-5649
語言英式英語
Web of Science 學科類別Mathematics; Mathematics, Applied; MATHEMATICS, APPLIED

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