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07/04/2022
Optimal numerical integration and approximation of functions on ℝ^d equipped with Gaussian measure
We investigate the numerical approximation of integrals over ℝ^d equippe...
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02/05/2022
Analyticity of Parametric and Stochastic Elliptic Eigenvalue Problems with an Application to Quasi-Monte Carlo Methods
In the present paper, we study the analyticity of the leftmost eigenvalu...
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01/06/2022
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
We establish summability results for coefficient sequences of Wiener-Her...
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11/10/2021
Deep ReLU neural network approximation of parametric and stochastic elliptic PDEs with lognormal inputs
We investigate non-adaptive methods of deep ReLU neural network approxim...
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03/01/2021
Computation complexity of deep ReLU neural networks in high-dimensional approximation
The purpose of the present paper is to study the computation complexity ...
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02/08/2021
High-dimensional nonlinear approximation by parametric manifolds in Hölder-Nikol'skii spaces of mixed smoothness
We study high-dimensional nonlinear approximation of functions in Hölder...
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07/17/2020
Sparse-grid sampling recovery and deep ReLU neural networks in high-dimensional approximation
We investigate approximations of functions from the Hölder-Zygmund space...
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05/31/2019