#### Filter Results:

#### Publication Year

2002

2016

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

- Josef Dick, Friedrich Pillichshammer Frontmatter, Friedrich Pillichshammer
- 2010

Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method,… (More)

We study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with general weights. These spaces are not necessarily tensor products of spaces of univariate functions. Sufficient conditions for tractability and strong tractability of multivariate integration in such weighted function spaces are found.… (More)

- Josef Dick, Frances Y Kuo, Ian H Sloan
- 2013

This paper is a contemporary review of QMC (" Quasi-Monte Carlo ") methods , i.e., equal-weight rules for the approximate evaluation of high dimensional integrals over the unit cube [0, 1] s , where s may be large, or even infinite. After a general introduction, the paper surveys recent developments in lattice methods, digital nets, and related themes.… (More)

This paper provides a novel approach to the construction of good lattice rules for the integration of Korobov classes of periodic functions over the unit s-dimensional cube. Theorems are proved which justify the construction of good lattice rules one component at a time – that is, the lattice rule for dimension s + 1 is obtained from the rule for dimension… (More)

A duality theory for digital nets, i.e., for finite points sets with strong uniformity properties, was introduced by Niederreiter and Pirsic. This duality theory is based on the concept of the dual space M of a digital net. In this paper we extend the duality theory from (finite) digital nets to (infinite) digital sequences. The analogue of the dual space… (More)