Daniel Kressner
ETH Zurich

Low rank tensor methods for solving high-dimensional linear systems
Linear systems arising from the discretization of high-dimensional problems are typically too large to be handled by standard algorithms. On the other hand, high-dimensional problems often feature a rather simple geometry and favorable smoothness properties. In such cases, it can be expected that the solution of the discretized system admits low rank tensor approximations. This talk presents numerical algorithms that operate with such low rank tensor ap- proximations and ideally scale only linearly (instead of exponentially) as the number of dimensions grows. It is shown how a combination of Krylov subspace and low rank techniques can be used to derive such algorithms. A number of examples, including parametrized and stochastic partial diff erential equations, illustrate the use of the newly developed algorithms in applications. This is joint work with Christine Tobler, ETH Zurich.