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 …
[ΒΙΒΛΙΟ][B] Monte carlo and quasi-monte carlo sampling
C Lemieux - 2009 - Springer
Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte
Carlo methods over the last two decades. Their successful implementation on practical …
Carlo methods over the last two decades. Their successful implementation on practical …
[ΒΙΒΛΙΟ][B] Numerical fourier analysis
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the
engineering, mathematical, and scientific communities with significant developments in …
engineering, mathematical, and scientific communities with significant developments in …
[ΒΙΒΛΙΟ][B] Tractability of Multivariate Problems: Standard information for functionals
E Novak, H Woźniakowski - 2008 - books.google.com
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 …
tractability of multivariate problems. The second volume deals with algorithms using …
[ΒΙΒΛΙΟ][B] Introduction to quasi-Monte Carlo integration and applications
G Leobacher, F Pillichshammer - 2014 - Springer
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 …
can be computed simply by computing iterated integrals, the attempt of doing so for a …
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 …
Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
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 …
matrix-vector notation so as to highlight its structural properties. For function spaces similar …
An historical overview of lattice point sets
Y Wang, FJ Hickernell - Monte Carlo and Quasi-Monte Carlo Methods …, 2002 - Springer
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 …
quadrature, simulation, experimental design, etc. The theoretical development of lattice point …
Minimax and maximin space-filling designs: some properties and methods for construction
L Pronzato - Journal de la Société Française de Statistique, 2017 - numdam.org
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 …
presented, and connections with other space-filling constructions are indicated. Several …