4 papers
A higher order lattice-based method for high-dimensional numerical integration using periodization
Felix Bartel, Alexander D. Gilbert, Michael Griebel +2
We present a novel numerical integration method for non-periodic functions over the high-dimensional unit cube by a specially crafted (unequally-)weighted quadrature rule…
Learning and Leveraging Anisotropy Parameters in ANOVA Approximation
Felix Bartel, Pascal Schröter
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anis…
Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate
Felix Bartel, Alexander D. Gilbert, Frances Y. Kuo +1
In this paper we show error bounds for randomly subsampled rank-1 lattices. We pay particular attention to the ratio of the size of the subset to the size of the initial lattice, w…
Sampling recovery in Bochner spaces and applications to parametric PDEs
Felix Bartel, Dinh Dũng
We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coeff…