Weighted Integral of Infinitely Differentiable Multivariate Functions is Exponentially Convergent

作     者：Guiqiao Xu Yongping Liu Jie Zhang 

作者机构：Department of MathematicsTianjin Normal UniversityTianjin300387PRC Department of MathematicsBeijing Normal UniversityBeijing100875PRC 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2019年第12卷第1期

页      面：98-114页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.11471043,11671271) by the Beijing Natural Science Foundation(Grant No.1172004) 

主　　题：Smolyak algorithm infinitely differentiable function class standard information worst case setting 

摘      要：We study the problem of a weighted integral of infinitely differentiable mul-tivariate functions defined on the unit cube with the L∞-norm of partial derivative of all orders bounded by *** consider the algorithms that use finitely many function values as information(called standard information).On the one hand,we obtained that the interpolatory quadratures based on the extended Chebyshev nodes of the second kind have almost the same quadrature *** the other hand,by using the Smolyak al-gorithm with the above interpolatory quadratures,we proved that the weighted integral problem is of exponential convergence in the worst case setting.