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

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 const...

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Hauptverfasser: Makoto, Matsumoto, Ohori, Ryuichi, Yoshiki, Takehito
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Sprache:eng
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Zusammenfassung: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.
DOI:10.48550/arxiv.1611.00561