Generalized Tractability for Multivariate Problems Part II: Linear Tensor Product Problems, Linear Information, and Unrestricted Tractability

摘要

We continue the study of generalized tractability initiated in our previous paper “Generalized tractability for multivariate problems, Part I: Linear tensor product problems and linear information”, J. Complex. 23:262–295, 2007. We study linear tensor product problems for which we can compute linear information which is given by arbitrary continuous linear functionals. We want to approximate an operator S d given as the d-fold tensor product of a compact linear operator S 1 for d=1,2,…, with ‖S 1‖=1 and S 1 having at least two positive singular values.