$\epsilon$-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs

Dinh Dũng, Michael Griebel, Vu Nhat Huy +1

In this article, we present a cost-benefit analysis of the approximation in tensor products of Hilbert spaces of Sobolev-analytic type. The Sobolev part is defined on a finite dime…