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Journal of Complexity, ISSN 0885-064X, 06/2018, Volume 46, pp. 103 - 112
In this paper we study tractability properties of the weighted star discrepancy with general coefficients of centered regular grids with different mesh-sizes.... 
Tractability | Quasi-Monte Carlo | Weighted star discrepancy | Regular grid | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | ALGORITHMS | MULTIVARIATE INTEGRATION
Journal Article
2010, ISBN 0521191599, xvii, 600
"This book is a comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory which starts from scratch... 
Sequences (Mathematics) | Monte Carlo method | Numerical integration | Nets (Mathematics) | Digital filters (Mathematics)
Book
Journal of Complexity, ISSN 0885-064X, 10/2019, p. 101441
We show that the isotropic discrepancy of a lattice point set can be bounded from below and from above in terms of the spectral test of the corresponding... 
Mathematics - Number Theory
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2014, Volume 83, Issue 287, pp. 1189 - 1206
We study multivariate integration for a weighted Korobov space of periodic infinitely many times differentiable functions for which the Fourier coefficients... 
Integers | Error rates | Mathematical theorems | Infinity | Differentiable functions | Polynomials | Necessary conditions | Function values | Fourier coefficients | Mathematical integration | MATHEMATICS, APPLIED
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2015, Volume 143, Issue 12, pp. 5043 - 5057
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2014, Volume 8865, pp. 173 - 184
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2019, Volume 350, pp. 46 - 54
We study the weighted star discrepancy of the Halton sequence. In particular, we show that the Halton sequence achieves strong polynomial tractability for the... 
Tractability | Digital sequence | Halton sequence | Quasi-Monte Carlo | Weighted star discrepancy | MATHEMATICS, APPLIED | BOUNDS | ALGORITHMS
Journal Article
2014, Compact Textbooks in Mathematics, ISBN 3319034251
This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive... 
Numerical analysis | Finance | Mathematics | Number theory
Web Resource
2014, Compact Textbooks in Mathematics, ISBN 3319034251
This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive... 
Numerical analysis | Finance | Mathematics | Number theory
Web Resource
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2018, Volume 56, Issue 2, pp. 684 - 707
We study the numerical approximation of integrals over R-s with respect to the standard Gaussian measure for integrands which lie in certain Hermite spaces of... 
Worst-case error | Numerical integration | Hermite polynomials | Higher order digital nets | MATHEMATICS, APPLIED | numerical integration | RULES | worst-case error | higher order digital nets
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2015, Volume 143, Issue 12, pp. 5043 - 5057
We prove bounds on the weighted star discrepancy of the p. This implies strong polynomial tractability for the weighted star discrepancy. We also show that a... 
MATHEMATICS | MATHEMATICS, APPLIED | ALGORITHMS | INTEGRATION | BOUNDS | STRONG TRACTABILITY
Journal Article
Numerical Algorithms, ISSN 1017-1398, 02/2019, Volume 80, Issue 2, pp. 661 - 685
The paper considers linear problems on weighted spaces of multivariate functions of many variables. The main questions addressed are the following: when is it... 
Multivariate problems | Truncation algorithms | Weighted function spaces | Truncation dimension | MATHEMATICS, APPLIED | Computer science | Analysis | Algorithms
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2017, Volume 145, Issue 8, pp. 3297 - 3310
We study high-dimensional numerical integration in the worst-case setting. The subject of tractability is concerned with the dependence of the worst-case... 
Tractability | Pseudorandom numbers | Quasi-Monte Carlo | Weighted star discrepancy | DIMENSIONALITY | MATHEMATICS | EXPONENTIAL-SUMS | MATHEMATICS, APPLIED | pseudorandom numbers | quasi-Monte Carlo | NUMERICAL-INTEGRATION | CURSE | tractability
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 9/2017, Volume 221, Issue 1, pp. 489 - 510
The L p -discrepancy is a quantitative measure for the irregularity of distribution modulo one of infinite sequences. In 1986, Proinov proved for all p > 1 a... 
Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | L-2 DISCREPANCY | VAN | SPACES | EXPLICIT CONSTRUCTIONS | NUMERICAL-INTEGRATION | IRREGULARITIES | RULES | CORPUT
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 07/2019, Volume 161, pp. 52 - 65
The paper considers truncation errors for functions of the form f(x1,x2,…)=g(∑j=1∞xjξj), i.e., errors of approximating f by fk(x1,…,xk)=g(∑j=1kxjξj), where the... 
Reproducing kernel | Average case error | Dimension truncation | Covariance kernel | Worst case error
Journal Article
Journal de Théorie des Nombres de Bordeaux, ISSN 1246-7405, 1/2019, Volume 31, Issue 1, pp. 179 - 204
Nous étudions la discrépance ( ϵ [1, ∞)) de réseaux digitaux de dimension 2. En 2001, Larcher et Pillichshammer ont identifié une classe de (0, , 2)-réseaux... 
Integers | Mathematical intervals | Mathematical sequences | Applied mathematics | Mathematical lattices | Dyadics | Indicator functions | Coefficients | Number theory
Journal Article
JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, ISSN 1246-7405, 2019, Volume 31, Issue 1, pp. 179 - 204
We study the L-p discrepancy of two-dimensional digital nets for finite p. In the year 2001 Larcher and Pillichshammer identified a class of digital nets for... 
MATHEMATICS | digital nets | L-p discrepancy | Hammersley net
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