This paper is a contemporary review of QMC ('quasi-Monte Carlo') methods, that is, equal-
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …

Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte
Carlo methods over the last two decades. Their successful implementation on practical …

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the
engineering, mathematical, and scientific communities with significant developments in …

This is the second volume of a three-volume set comprising a comprehensive study of the
tractability of multivariate problems. The second volume deals with algorithms using …

While Fubini's theorem states that the integral of a function on the s-dimensional unit cube
can be computed simply by computing iterated integrals, the attempt of doing so for a …

This article provides a survey of recent research efforts on the application of quasi-Monte
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …

We present some results on the complexity of numerical integration. We start with the
seminal paper of Bakhvalov (1959) and end with new results on the curse of dimensionality …

We reformulate the original component-by-component algorithm for rank-$1 $ lattices in a
matrix-vector notation so as to highlight its structural properties. For function spaces similar …

Good lattice point sets are an important kind of low discrepancy points for multidimensional
quadrature, simulation, experimental design, etc. The theoretical development of lattice point …

A few properties of minimax and maximin optimal designs in a compact subset of Rd are
presented, and connections with other space-filling constructions are indicated. Several …