Low-rank techniques for paramater-dependent problems

We consider linear systems and eigenvalue problems depending on one or several parameters, as they arise from the discretization of parameter-dependent partial differential equations or in eigenvalue optimization problems. There exist a number of established techniques in numerical linear algebra for dealing with parameter-dependent problems, such as subspace recycling. However, these techniques do not fully benefit from the fact that the solution to such problems usually depends smoothly on the parameter(s). We show how low-rank matrix and tensor techniques can be used to implicitly benefit from smoothness and reduce the computational effort, sometimes drastically. This is based on joint work with Christine Tobler and Bart Vandereycken.