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

2016/11/02 by Makoto Matsumoto, Makoto, Matsumoto, Ryuichi Ohori +3
Mathematics · Computer Science · #Mathematical Approximation and Integration #Digital Image Processing Techniques #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.1611.00561

Abstract

In this paper, we consider Quasi-Monte Carlo (QMC) worst case error of weighted smooth function classes in C^∞[0,1]^s by a digital net over \mathbb F₂. 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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