Optimization of Approximate Solution of Integral Equations of Several Variables  

作　　者：Wan MA Xing Hua WANG Department of Mathematics, Zhejiang University. Hangzhou 310028, P. R. China 

出　　处：《Acta Mathematica Sinica,English Series》2002年第3期455-462,共8页数学学报（英文版）

基　　金：This work is supported by the Special Funds for Major State Basic Research Projects (Grant No. G19990328);the Zhejiang Provincial Natural Science Foundation (Grant No. 100002).

摘　　要：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.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.

关 键 词：Integral equations Direct methods Anisotropic Sobolev classes 

分 类 号：O175.5[理学—数学]