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08/11/2023
Doubling the rate – improved error bounds for orthogonal projection in Hilbert spaces
Convergence rates for L_2 approximation in a Hilbert space H are a centr...
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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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03/31/2023
Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions
We describe a fast method for solving elliptic partial differential equa...
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12/22/2022
Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation
In this paper we propose and analyse a method for estimating three quant...
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10/31/2022
Uncertainty quantification for random domains using periodic random variables
We consider uncertainty quantification for the Poisson problem subject t...
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08/04/2022
Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
We study the application of a tailored quasi-Monte Carlo (QMC) method to...
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07/26/2022
Needlets Liberated
Spherical needlets were introduced by Narcowich, Petrushev, and Ward to ...
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12/22/2021
Preintegration is not smoothing when monotonicity fails
Preintegration is a technique for high-dimensional integration over d-di...
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12/20/2021
Approximating distribution functions and densities using quasi-Monte Carlo methods after smoothing by preintegration
The cumulative distribution or probability density of a random variable,...
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03/30/2021
Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on ℝ^d
We prove that a variant of the classical Sobolev space of first-order do...
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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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07/13/2020
Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification
This paper deals with the kernel-based approximation of a multivariate p...
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04/26/2020
Quasi-Monte Carlo finite element analysis for wave propagation in heterogeneous random media
We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient...
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10/22/2019
A quasi-Monte Carlo Method for an Optimal Control Problem Under Uncertainty
We study an optimal control problem under uncertainty, where the target ...
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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