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SIAM Journal on Scientific Computing, ISSN 1064-8275, 2006, Volume 28, Issue 6, pp. 2162 - 2188
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 2/2018, Volume 197, Issue 1, pp. 109 - 126
We prove upper bounds on the order of convergence of lattice-based algorithms for numerical integration in function spaces of dominating mixed smoothness on... 
65D30 | 11K31 | Rank-1 lattice points | Numerical integration | Kronecker lattice | 65D32 | Mathematics, general | Mathematics | Quasi-Monte Carlo | Zaremba index | Besov space | QUADRATURE-FORMULAS | MATHEMATICS, APPLIED | CUBATURE FORMULAS | NUMBERS | APPROXIMATION | OPTIMAL COEFFICIENTS | MATHEMATICS | MULTIPLE INTEGRATION | DISCREPANCY | ERROR | RULES | BY-COMPONENT CONSTRUCTION | Monte Carlo method | Analysis | Algorithms
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 05/2016, Volume 496, pp. 438 - 451
Characterisations are provided of the Hermite normal form of certain integer circulant and skew-circulant matrices. These matrices are associated with rank-1... 
Hermite normal form | Rank-1 circulant lattice rules | Rank-1circulant lattice rules | MATHEMATICS | MATHEMATICS, APPLIED | MATRICES | Online searching | Rankings | Internet/Web search services | Database searching
Journal Article
Mathematics of Computation, ISSN 0025-5718, 4/2006, Volume 75, Issue 254, pp. 903 - 920
Journal Article
Journal of Complexity, ISSN 0885-064X, 10/2016, Volume 36, pp. 166 - 181
Journal Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 11/2016, Volume 41, Issue 3, pp. 713 - 748
In this paper, we suggest approximate algorithms for the reconstruction of sparse high-dimensional trigonometric polynomials, where the support in frequency... 
Trigonometric polynomials | Lattice rule | Sparse fast Fourier transform | Rank-1 lattice | FFT | Approximation of multivariate functions | MATHEMATICS, APPLIED | PURSUIT | GRIDS | PARAMETER-ESTIMATION | FOURIER-TRANSFORM | STABILITY | Cytokinins | Algorithms
Journal Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 11/2019, Volume 47, Issue 3, pp. 702 - 729
The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency... 
Sparse multivariate trigonometric polynomials | Lattice rule | Multiple rank-1 lattice | Fast Fourier transform | MATHEMATICS, APPLIED | PERIODIC-FUNCTIONS | APPROXIMATION | RANK-1 LATTICE
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 04/2007, Volume 76, Issue 258, pp. 989 - 1004
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 2/2018, Volume 24, Issue 1, pp. 17 - 44
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 10/2019, Volume 246, pp. 1 - 27
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize... 
Trigonometric polynomials | Lattice rule | Generalized hyperbolic cross | Fast Fourier transform | Approximation of multivariate periodic functions | Multiple rank-1 lattice | Generalized mixed smoothness | MATHEMATICS | ALGORITHMS | Algorithms
Journal Article
Journal of Complexity, ISSN 0885-064X, 2006, Volume 22, Issue 1, pp. 4 - 28
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 232, Issue 2, pp. 240 - 251
We approximate weighted integrals over Euclidean space by using shifted rank-1 lattice rules with good bounds on the “generalised weighted star discrepancy”.... 
Component-by-component construction | Generalised weighted star discrepancy | Rank-1 lattice rules | MATHEMATICS, APPLIED | UNBOUNDED INTEGRANDS | CONSTRUCTION | ALGORITHMS | MULTIVARIATE INTEGRATION | STRONG TRACTABILITY
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 3, pp. A1436 - A1450
Journal Article
Journal of Complexity, ISSN 0885-064X, 06/2015, Volume 31, Issue 3, pp. 424 - 456
In this paper, we present error estimates for the approximation of multivariate periodic functions in periodic Hilbert spaces of isotropic and dominating mixed... 
Hyperbolic cross | Trigonometric polynomials | Lattice rule | Rank-1 lattice | Approximation of multivariate functions | Fast Fourier transform | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | FOURIER-TRANSFORM | SPACES | SPARSE GRIDS
Journal Article
Constructive Approximation, ISSN 0176-4276, 4/2017, Volume 45, Issue 2, pp. 311 - 344
We study multivariate integration of functions that are invariant under the permutation (of a subset) of their arguments. Recently, in Nuyens et al. (Adv... 
68Q25 | 68W40 | Numerical integration | Mathematics | 65Y20 | Quasi-Monte Carlo methods | Quadrature | 65D30 | Cubature | Numerical Analysis | Analysis | 65D32 | 65C05 | Component-by-component construction | Rank-1 lattice rules | APPROXIMATION | MATHEMATICS | WEIGHTED SOBOLEV SPACES | ACHIEVE | COMPLEXITY | GOOD LATTICE RULES | BY-COMPONENT CONSTRUCTION | Computer science | Monte Carlo method | Algorithms | Resveratrol
Journal Article
Numerical Algorithms, ISSN 1017-1398, 2/2012, Volume 59, Issue 2, pp. 161 - 183
Quasi-Monte Carlo integration rules, which are equal-weight sample averages of function values, have been popular for approximating multivariate integrals due... 
Digital nets and sequences | Algebra | Algorithms | Numerical integration | Computer Science | Numeric Computing | Mathematics, general | Theory of Computation | Lattice rules and sequences | Quasi-Monte Carlo | Higher order convergence | MATHEMATICS, APPLIED | RANK-1 LATTICE RULES | BY-COMPONENT CONSTRUCTION
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 01/2018, Volume 143, pp. 202 - 214
Journal Article
Journal of Complexity, ISSN 0885-064X, 02/2016, Volume 32, Issue 1, pp. 74 - 80
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several... 
Lattice point sets | Component-by-component algorithm | Polynomial lattice point sets | MATHEMATICS, APPLIED | RANK-1 LATTICE RULES | SPACES | EQUATIONS | WEIGHTED KOROBOV | ALGORITHMS | MATHEMATICS | QUASI-MONTE CARLO | INTEGRATION | CONVERGENCE | POINTS | Algorithms
Journal Article
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