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arXiv · 1611.00561

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

Matsumoto Makoto·Ryuichi Ohori·Takehito Yoshiki
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Abstract

In this paper, we consider Quasi-Monte Carlo (QMC) worst case error of weighted smooth function classes in $C^\infty[0,1]^s$ by a digital net over $\mathbb F_2$. 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.

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Matsumoto Makoto, Ryuichi Ohori, Takehito Yoshiki. 2016-11-02. Approximation of Quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions. https://arxiv.org/abs/1611.00561

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