Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs

We investigate the convergence rate of approximations by finite sums of rank-1 tensors of solutions of multiparametric elliptic PDEs. Such PDEs arise, for example, in the parametric, deterministic reformulation of elliptic PDEs with random field inputs, based, for example, on the Mterm truncated Karhunen-Loeve expansion. Our approach could be regarded as either a class of compressed approximations of these solutions or as a new class of...