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Quasi-Monte Carlo integration of functions of unbounded variation

Ronald F. A. Cools, Tim Pillards

Published Sep 1, 2006• 0 citations
OpenAlex

Abstract

qMC integration of functions of unbounded variation Quasi-Monte Carlo Functions of unbounded variation Conclusion

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We examine the problem of numerically estimating the integral of a function f. The classical approaches to this problem are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate f and have error , where σ(f ) is the standard deviation of f. QMC methods are based on evaluating f at explicit point sets with low discrepancy, and as given by the classical Koksma- Hlawka inequality, they have error Õ (σHK(f )/n ), where σΗΚ(f ) is the variation of f in the sense of Hardy and Krause. These two methods have distinctive advantages and shortcomings, and a fundamental question is to find a method that combines the advantages of both.