Approximation of Quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions

被引：1

作者：

Matsumoto, Makoto ^{[1
]}

Ohori, Ryuichi ^{[2
]}

Yoshiki, Takehito ^{[3
]}

机构：

[1] Hiroshima Univ, Grad Sch Sci, Hiroshima 7398526, Japan

[2] Fujitsu Labs Ltd, Kawasaki, Kanagawa 2118588, Japan

[3] Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Kyoto 6068561, Japan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 330卷

关键词：

Quasi-Monte Carlo integration; Digital net; Worst case error; Walsh coefficients; Infinitely differentiable functions; POINT SETS; MULTIVARIATE INTEGRATION; DIGITAL NETS; RULES; WAFOM;

D O I：

10.1016/j.cam.2017.08.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider Quasi-Monte Carlo (QMC) worst case error of weighted smooth function classes in C-infinity [0, 1](s) ns by a digital net over F-2. We show that the ratio of the worst case error to the QMC integration error of an exponential function is bounded above and below by constants. This result provides us with a simple interpretation that a digital net with small QMC integration error for an exponential function also gives the small integration error for any function in this function space. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：155 / 164

页数：10

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