Tractability of $\mathbb{L}_2$approximation in hybrid function spaces
Abstract
We consider multivariate $\mathbb{L}_2$approximation in reproducing kernel Hilbert spaces which are tensor products of weighted Walsh spaces and weighted Korobov spaces. We study the minimal worstcase error $e^{\mathbb{L}_2\mathrm{app},\Lambda}(N,d)$ of all algorithms that use $N$ information evaluations from the class $\Lambda$ in the $d$dimensional case. The two classes $\Lambda$ considered in this paper are the class $\Lambda^{\rm all}$ consisting of all linear functionals and the class $\Lambda^{\rm std}$ consisting only of function evaluations. The focus lies on the dependence of $e^{\mathbb{L}_2\mathrm{app},\Lambda}(N,d)$ on the dimension $d$. The main results are conditions for weak, polynomial, and strong polynomial tractability.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 DOI:
 10.48550/arXiv.1701.02910
 arXiv:
 arXiv:1701.02910
 Bibcode:
 2017arXiv170102910K
 Keywords:

 Mathematics  Numerical Analysis;
 41A25;
 41A63;
 65D15;
 65Y20