High-dimensional integration: the quasi-Monte Carlo way
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 …
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …
Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation
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 …
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …
Some results on the complexity of numerical integration
E Novak - Monte Carlo and Quasi-Monte Carlo Methods: MCQMC …, 2016 - Springer
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 …
seminal paper of Bakhvalov (1959) and end with new results on the curse of dimensionality …
Unveiling the power of stochastic methods: Advancements in air pollution sensitivity analysis of the digital twin
Thorough examination of various aspects related to the distribution of air pollutants in a
specific region and the factors contributing to high concentrations is essential, as these …
specific region and the factors contributing to high concentrations is essential, as these …
Higher order QMC Petrov--Galerkin discretization for affine parametric operator equations with random field inputs
We construct quasi--Monte Carlo methods to approximate the expected values of linear
functionals of Petrov--Galerkin discretizations of parametric operator equations which …
functionals of Petrov--Galerkin discretizations of parametric operator equations which …
Innovative digital stochastic methods for multidimensional sensitivity analysis in air pollution modelling
Nowadays, much of the world has a regional air pollution strategy to limit and decrease the
pollution levels across governmental borders and control their impact on human health and …
pollution levels across governmental borders and control their impact on human health and …
Construction-free median quasi-Monte Carlo rules for function spaces with unspecified smoothness and general weights
T Goda, P L'ecuyer - SIAM Journal on Scientific Computing, 2022 - SIAM
We study quasi-Monte Carlo (QMC) integration of smooth functions defined over the
multidimensional unit cube. Inspired by a recent work of Pan and Owen, we study a new …
multidimensional unit cube. Inspired by a recent work of Pan and Owen, we study a new …
Higher order quasi--Monte Carlo integration for holomorphic, parametric operator equations
We analyze the convergence of higher order quasi--Monte Carlo (QMC) quadratures of
solution functionals to countably parametric, nonlinear operator equations with distributed …
solution functionals to countably parametric, nonlinear operator equations with distributed …
Discrepancy theory and quasi-Monte Carlo integration
J Dick, F Pillichshammer - A panorama of discrepancy theory, 2014 - Springer
In this chapter we show the deep connections between discrepancy theory on the one hand
and quasi-Monte Carlo integration on the other. Discrepancy theory was established as an …
and quasi-Monte Carlo integration on the other. Discrepancy theory was established as an …
A tool for custom construction of QMC and RQMC point sets
P L'Ecuyer, P Marion, M Godin… - … Conference on Monte …, 2020 - Springer
Abstract We present LatNet Builder, a software tool to find good parameters for lattice rules,
polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and …
polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and …