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 …

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 …

In this paper quasi-Monte Carlo (QMC) methods are applied to a class of elliptic partial
differential equations (PDEs) with random coefficients, where the random coefficient is …

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 …

In this paper we analyze the numerical approximation of diffusion problems over polyhedral
domains in R^ d R d (d= 1, 2, 3 d= 1, 2, 3), with diffusion coefficient a (x, ω) a (x, ω) given as …

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 …

Lattice rules are particular instances of quasi-Monte Carlo rules for numerical integration of
functions over the 𝑑-dimensional unit cube [0, 1] 𝑑, where the emphasis lies on high …

This paper is a sequel to our previous work (Kuo et al. in SIAM J Numer Anal, 2012) where
quasi-Monte Carlo (QMC) methods (specifically, randomly shifted lattice rules) are applied to …

Lattice rules are a family of equal-weight cubature formulae for approximating high-
dimensional integrals. By now it is well established that good generating vectors for lattice …