Multi- and infinite-variate integration and 𝐿²-approximation on Hilbert spaces with Gaussian kernels
Year: 2026
Type: article
Abstract: We study integration and L 2 L^2 -approximation in the worst-case setting for deterministic linear algorithms based on function evaluations. The underlying function space is a reproducing kernel Hilbert space with a Gaussian kernel of tensor product form. In the infinite-variate case, for both computational problems, we establish matching upper and lower bounds for the polynomial convergence rate of the n n -th minimal error. In the multivariate case, we improve several tractability results for the integration problem. For the proofs, we establish the following transference result together with an explicit construction: Each of the computational problems on a space with a Gaussian kernel is equivalent on the level of algorithms to the same problem on a Hermite space with suitable parameters.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4191
Authors: M. Gnewuch, K. Ritter, R. Rüßmann
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7123337624