Zobrazeno 1 - 10
of 349
pro vyhledávání: '"Dick, Josef"'
We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured
Externí odkaz:
http://arxiv.org/abs/2409.12879
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on the parametr
Externí odkaz:
http://arxiv.org/abs/2409.00893
Publikováno v:
Journal of Scientific Computing, 2024
We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~$\alpha \in (0,1)$. The basic idea of our scheme is based on local integration followed by linear interpola
Externí odkaz:
http://arxiv.org/abs/2401.04946
We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equation in engineering and physics, the stochastic Landau-Lifshitz-Gilbe
Externí odkaz:
http://arxiv.org/abs/2310.11225
We study the approximation of integrals $\int_D f(\boldsymbol{x}^\top A) \mathrm{d} \mu(\boldsymbol{x})$, where $A$ is a matrix, by quasi-Monte Carlo (QMC) rules $N^{-1} \sum_{k=0}^{N-1} f(\boldsymbol{x}_k^\top A)$. We are interested in cases where t
Externí odkaz:
http://arxiv.org/abs/2305.11645
We study numerical integration over bounded regions in $\mathbb{R}^s, s\ge1$ with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, where the underlying point set is derived from deterministic constructio
Externí odkaz:
http://arxiv.org/abs/2304.14786
Publikováno v:
Mathematics of Computation, Volume 91, Issue 338, 2771-2801, 2022
We study a randomized quadrature algorithm to approximate the integral of periodic functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens and Ullrich (2019) shows that rank-1 lattice rules with a randomly chosen nu
Externí odkaz:
http://arxiv.org/abs/2109.11694
Publikováno v:
In Journal of Computational and Applied Mathematics April 2024 440