Average case tractability of a multivariate approximation problem

被引：17
作者：
Liu, Yongping [1 ]
Xu, Guiqiao [2 ]
机构：
[1] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China
[2] Tianjin Normal Univ, Dept Math, Tianjin 300387, Peoples R China
来源：
JOURNAL OF COMPLEXITY | 2017年 / 43卷
关键词：
Tractability; EC-tractability; Korobov kernel; Linear problem; Eigenvalue; Average case setting; KOROBOV SPACES; EXPONENTIAL CONVERGENCE; INTEGRATION;
D O I：
10.1016/j.jco.2017.08.002
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Many authors have studied exponentially-convergent tractability (EC-tractability) in the worst case setting. Here, we study EC-tractability in the average case setting. Our problem is multivariate approximation over the space of continuous real functions equipped with a zero-mean Gaussian measure whose covariance kernel is given as a Korobov kernel. We obtain necessary and sufficient conditions for certain kinds of tractability, including EC-tractability. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：76 / 102
页数：27
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