Zobrazeno 1 - 10
of 422
pro vyhledávání: '"Harbrecht, Helmut"'
The present article is concerned with the nonlinear approximation of functions in the Sobolev space H^q with respect to a tensor-product, or hyperbolic wavelet basis on the unit n-cube. Here, q is a real number, which is not necessarily positive. We
Externí odkaz:
http://arxiv.org/abs/2411.04837
In scattered data approximation, the span of a finite number of translates of a chosen radial basis function is used as approximation space and the basis of translates is used for representing the approximate. However, this natural choice is by no me
Externí odkaz:
http://arxiv.org/abs/2408.11389
The present article is dedicated to proving convergence of the stochastic gradient method in case of random shape optimization problems. To that end, we consider Bernoulli's exterior free boundary problem with a random interior boundary. We recast th
Externí odkaz:
http://arxiv.org/abs/2408.05021
Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation
On a finite time interval $(0,T)$, we consider the multiresolution Galerkin discretization of a modified Hilbert transform $\mathcal H_T$ which arises in the space-time Galerkin discretization of the linear diffusion equation. To this end, we design
Externí odkaz:
http://arxiv.org/abs/2402.10346
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we derive very eff
Externí odkaz:
http://arxiv.org/abs/2402.09531
This article is concerned with a regularity analysis of parametric operator equations with a perspective on uncertainty quantification. We study the regularity of mappings between Banach spaces near branches of isolated solutions that are implicitly
Externí odkaz:
http://arxiv.org/abs/2310.01256
We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft scatterers. These in
Externí odkaz:
http://arxiv.org/abs/2306.11324
We consider scattered data approximation in samplet coordinates with $\ell_1$-regularization. The application of an $\ell_1$-regularization term enforces sparsity of the coefficients with respect to the samplet basis. Samplets are wavelet-type signed
Externí odkaz:
http://arxiv.org/abs/2306.10180
We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently introduced by Kaarnioja, Kuo, and Sloan (SIAM J. Numer. Anal., 2020) in
Externí odkaz:
http://arxiv.org/abs/2210.17329
Let $\Omega_i\subset\mathbb{R}^{n_i}$, $i=1,\ldots,m$, be given domains. In this article, we study the low-rank approximation with respect to $L^2(\Omega_1\times\dots\times\Omega_m)$ of functions from Sobolev spaces with dominating mixed smoothness.
Externí odkaz:
http://arxiv.org/abs/2203.04100