Optimization of Approximate Solution of Integral Equations of Several Variables |
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Authors: | Wan Ma Xing Hua Wang |
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Affiliation: | (1) Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China E-mail: mwxx10@263.net, wangxh@mail.hz.zj.cn, CN |
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Abstract: | In this paper, we consider the problem of optimization of adaptive direct methods of operator equations. Adaptivity of a direct method is understood in the sense that the subspace on the basis of which it is constructed is chosen depending on the operator of the concrete equation (otherwise, nonadaptive direct method is then concerned), which would essentially let us increase the precision. For some classes of the second kind of Fredhlom integral equations with anisotropic smooth kernels we determine the exact order of the error of adaptive direct methods, and we also give an optimal algorithm. Received April 13, 2001, Accepted September 13, 2001 |
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Keywords: | Integral equations Direct methods Anisotrophic Sobolev classes |
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