Average case tractability of multivariate approximation with Gevrey type kernels

TL;DR

This paper studies the average case complexity of multivariate approximation problems using Gevrey kernels, providing conditions for different tractability notions based on problem parameters.

Contribution

It offers a comprehensive analysis of algebraic and exponential tractability for multivariate approximation with Gevrey kernels, including necessary and sufficient conditions.

Findings

Conditions for algebraic tractability derived

Conditions for exponential tractability established

Analysis based on covariance kernel parameters

Abstract

We consider multivariate approximation problems in the average case setting with a zero mean Gaussian measure whose covariance kernel is a periodic Gevrey kernel. We investigate various notions of algebraic tractability and exponential tractability, and obtain necessary and sufficient conditions in terms of the parameters of the problem.