2014, ISBN 1107074002, ix, 335

Book

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

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)

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

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

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

7.
Full Text
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers

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

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

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

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

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

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

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

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

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

16.
Full Text
Truncation in average and worst case settings for special classes of ∞-variate functions

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

Reproducing kernel | Average case error | Dimension truncation | Covariance kernel | Worst case error

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2014, Volume 162, Issue 1, pp. 65 - 99

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

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

MATHEMATICS | digital nets | L-p discrepancy | Hammersley net

Journal Article

Numerische Mathematik, ISSN 0029-599X, 2/2014, Volume 126, Issue 2, pp. 259 - 291

The aim of this paper is to show that one can achieve convergence rates of $$N^{-\alpha + \delta }$$ N − α + δ for $$\alpha > 1/2$$ α > 1 / 2 (and for $$\delta...

65D30 | Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65D32 | Appl.Mathematics/Computational Methods of Engineering | 11K36 | Numerical and Computational Physics | Mathematics, general | 11K16 | Mathematics | MONTE CARLO METHODS | MATHEMATICS, APPLIED | CUBATURE FORMULAS | ACHIEVE | IMBEDDED FAMILY | NUMERICAL-INTEGRATION | DISCREPANCY | WEIGHTED KOROBOV | ALGORITHMS | CONVERGENCE RATE | BY-COMPONENT CONSTRUCTION | Computer science

65D30 | Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65D32 | Appl.Mathematics/Computational Methods of Engineering | 11K36 | Numerical and Computational Physics | Mathematics, general | 11K16 | Mathematics | MONTE CARLO METHODS | MATHEMATICS, APPLIED | CUBATURE FORMULAS | ACHIEVE | IMBEDDED FAMILY | NUMERICAL-INTEGRATION | DISCREPANCY | WEIGHTED KOROBOV | ALGORITHMS | CONVERGENCE RATE | BY-COMPONENT CONSTRUCTION | Computer science

Journal Article

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