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THE WORST CASE COMPLEXITY OF THE FREDHOLM EQUATION OF THE SECOND KIND WITH FREE TERM IN H'(Г)
引用本文:蒋田仔.THE WORST CASE COMPLEXITY OF THE FREDHOLM EQUATION OF THE SECOND KIND WITH FREE TERM IN H''''(Г)[J].高等学校计算数学学报(英文版),1997(2).
作者姓名:蒋田仔
作者单位:Jiang Tian-zi School of Mathematics,The University of New South Wales,Sydney 2052,Australia and National Laboratory of Pattern Recognition,Institute of Automation Chinese Academy of Sciences,Beijing 100080,PRC
基金项目:This work was partially supported by the Chinese National Science Fundation,the Chinese National High Technology Program(863).and the UNSW Vice-Chancellor's Post Doctoral Fellowship in Australia.
摘    要:This paper deals with the approximate solution of the Fredholm equation Lu= f of the second kind with f ∈H'(Γ). First, we give the order of the n-the optimal radius in the worst case setting. Then, we show that the Galerkin method using 2n+1 inner products of f has minimal error. Finally, we give the estimate of the ε-complexity of the Fredholm problem of the second kind and Galerkin method in the worst case setting.

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