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 …

This book provides a systematic survey of classical and recent results on hyperbolic cross
approximation. Motivated by numerous applications, the last two decades have seen great …

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 review the basic principles of quasi-Monte Carlo (QMC) methods, the randomizations
that turn them into variance-reduction techniques, the integration error and variance bounds …

We construct quasi--Monte Carlo methods to approximate the expected values of linear
functionals of Petrov--Galerkin discretizations of parametric operator equations which …

This book is a survey on multivariate approximation. The 20th century was a period of
transition from univariate problems to multivariate problems in a number of areas of …

We define a Walsh space which contains all functions whose partial mixed derivatives up to
order δ≥1 exist and have finite variation. In particular, for a suitable choice of parameters …

We analyze the convergence of higher order quasi--Monte Carlo (QMC) quadratures of
solution functionals to countably parametric, nonlinear operator equations with distributed …

Kernel-based quadrature rules are becoming important in machine learning and statistics,
as they achieve super-$¥ sqrt {n} $ convergence rates in numerical integration, and thus …