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08/22/2023
Dynamically Orthogonal Approximation for Stochastic Differential Equations
In this paper, we set the mathematical foundations of the Dynamical Low ...
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12/22/2022
Randomizing the trapezoidal rule gives the optimal RMSE rate in Gaussian Sobolev spaces
Randomized quadratures for integrating functions in Sobolev spaces of or...
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02/23/2022
Sub-optimality of Gauss–Hermite quadrature and optimality of trapezoidal rule for functions with finite smoothness
A sub-optimality of Gauss–Hermite quadrature and an optimality of the tr...
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08/28/2021
Density estimation in RKHS with application to Korobov spaces in high dimensions
A kernel method for estimating a probability density function (pdf) from...
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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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06/09/2020
Stability properties of a projector-splitting scheme for the dynamical low rank approximation of random parabolic equations
We consider the Dynamical Low Rank (DLR) approximation of random parabol...
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02/06/2020