The information-based complexity of approximation problem by adaptive Monte Carlo methods  

作　　者：FANG GenSun DUAN LiQin 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,China

出　　处：《Science China Mathematics》2008年第9期1679-1689,共11页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 10671019);the Research Fund for the Doctoral Program of Higher Education (Grant No. 20050027007)

摘　　要：In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \mathbb{T}^d $ ), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MWpr,α(Td), 1 < p < ∞, in the norm of Lq(Td), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.

关 键 词：adaptive Monte Carlo method Sobolev space with bounded mixed derivative asymptotic order 41A46 41A63 65C05 65D99 

分 类 号：O242.2[理学—计算数学]