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08/06/2023
A randomised lattice rule algorithm with pre-determined generating vector and random number of points for Korobov spaces with 0 < α≤ 1/2
In previous work (Kuo, Nuyens, Wilkes, 2023), we showed that a lattice r...
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04/20/2023
Random-prime–fixed-vector randomised lattice-based algorithm for high-dimensional integration
We show that a very simple randomised algorithm for numerical integratio...
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04/04/2023
Comparison of Two Search Criteria for Lattice-based Kernel Approximation
The kernel interpolant in a reproducing kernel Hilbert space is optimal ...
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09/02/2022
Constructing Embedded Lattice-based Algorithms for Multivariate Function Approximation with a Composite Number of Points
We approximate d-variate periodic functions in weighted Korobov spaces w...
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08/28/2021
Scaled lattice rules for integration on ℝ^d achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces
We show that to approximate the integral ∫_ℝ^d f(x) dx one can simply us...
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11/10/2020
Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory
High dimensional integrals are abundant in many fields of research inclu...
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01/09/2020
Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness
Lattice rules are among the most prominently studied quasi-Monte Carlo m...
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10/15/2019
Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights
In a recent paper by the same authors, we provided a theoretical foundat...
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10/15/2019
Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters
This paper provides the theoretical foundation for the construction of l...
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08/03/2019
Function integration, reconstruction and approximation using rank-1 lattices
We consider rank-1 lattices for integration and reconstruction of functi...
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07/29/2019
Enhanced Multi-Index Monte Carlo by means of Multiple Semi-Coarsened Multigrid for Anisotropic Diffusion Problems
In many models used in engineering and science, material properties are ...
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04/30/2019
MDFEM: Multivariate decomposition finite element methods for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM
We introduce the novel multivariate decomposition finite element method ...
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12/19/2017