Optimization on class of operator equations in the probabilistic case setting  

作　　者：Gen-sun FANG Li-xin QIAN 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China [2]College of Mathematics and Physics,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Science China Mathematics》2007年第1期100-104,共5页中国科学：数学（英文版）

基　　金：This work was partially supported by the National Natural Science Foundation of China (Grant No. 10371009);Research Fund for the Doctoral Program Higher Education (Grant No. 20050027007).

摘　　要：In this paper, we introduce a problem of the optimization of approximate solutions of operator equations in the probabilistic case setting, and prove a general result which connects the relation between the optimal approximation order of operator equations with the asymptotic order of the probabilistic width. Moreover, using this result, we determine the exact orders on the optimal approximate solutions of multivariate Freldholm integral equations of the second kind with the kernels belonging to the multivariate Sobolev class with the mixed derivative in the probabilistic case setting.In this paper, we introduce a problem of the optimization of approximate solutions of operator equations in the probabilistic case setting, and prove a general result which connects the relation between the optimal approximation order of operator equations with the asymptotic order of the probabilistic width. Moreover, using this result, we determine the exact orders on the optimal approximate solutions of multivariate Preldholm integral equations of the second kind with the kernels belonging to the multivariate Sobolev class with the mixed derivative in the probabilistic case setting.

关 键 词：probabilistic width Gauss measure multivariate Sobolev space operator equation 41A46 41A63 45L05 60G15 

分 类 号：O177[理学—数学]