Numerical tensor calculus with application to the stochastic Galerkin matrix


Professor Wolfgang Hackbusch


Max Planck Institute for Mathematics in the Sciences, Germany


Fri, 27/11/2015 - 11:05am to 11:55am


RC-M032, The Red Centre, UNSW


The numerical tensor calculus is an efficient tool for treating high-dimensional objects. The tensor formats involve certain representation ranks. The crucial question is the relation between these ranks and the approximation error. The application problem is a diffusion problem whose conductivity coefficient is a log-normal random field. Under suitable assumptions we prove that the approximation error depends only on the smoothness of the covariance function and does neither depend on the number of random variables nor on the degree of the multivariate Hermite polynomials.