The State of the Art in Quasi-Monte Carlo Methods

Abstract

Abstract. In this article we give a survey on quasi-Monte Carlo (QMC) methods, which are a class of high-dimensional numerical integration methods. We start from the classical QMC theory and construction of point sets based on the uniform distribution theory, and then move on to more recent progresses on QMC theory, such as the worst-case error for reproducing kernel Hilbert spaces, construction of special classes of QMC point sets called lattice point sets and digital nets, and their randomization techniques. Finally we show the effectiveness of QMC methods through a series of numerical experiments.