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.
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)
