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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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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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01/31/2023
Application of dimension truncation error analysis to high-dimensional function approximation
Parametric mathematical models such as partial differential equations wi...
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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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09/13/2022
Generalized dimension truncation error analysis for high-dimensional numerical integration: lognormal setting and beyond
Partial differential equations (PDEs) with uncertain or random inputs ha...
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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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07/15/2022
Quasi-Monte Carlo and discontinuous Galerkin
In this study, we design and develop Quasi-Monte Carlo (QMC) cubatures f...
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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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10/22/2019