Exponential convergence-tractability of general linear problems in the average case setting

Abstract

We study d-variate general linear problems defined over Hilbert spaces in the average case setting. We consider algorithms that use finitely many evaluations of arbitrary linear functionals. We obtain the necessary and sufficient conditions for Exponential Convergence-(Strong) Polynomial Tractability, Quasi-Polynomial Tractability and (Uniform) Weak Tractability. All results are in terms of the eigenvalues of the corresponding covariance operators.