research
∙
09/10/2023
Sparse-grid sampling recovery and numerical integration of functions having mixed smoothness
We give a short survey of recent results on sparse-grid linear algorithm...
share
research
∙
08/19/2022
Numerical weighted integration of functions having mixed smoothness
We investigate the approximation of weighted integrals over ℝ^d for inte...
research
∙
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...
research
∙
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...
research
∙
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...
research
∙
11/10/2021
Collocation approximation by deep neural ReLU networks for parametric elliptic PDEs with lognormal inputs
We obtained convergence rates of the collocation approximation by deep R...
research
∙
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 ...
research
∙
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...
research
∙
12/15/2020
Approximation by linear combinations of translates of a single function
We study approximation by arbitrary linear combinations of n translates ...
research
∙
07/17/2020