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ALOP Colloquium with Prof. Andreas Frommer
15. May 2017 / 16:00 - 18:00
On Monday, May 15 2017, Prof. Andreas Frommer of Bergische Universität Wuppertal will join the ALOP-Colloquium and present his recent work entitled
Matrix functions – computation and convergence for Krylov subspace based methods
Abstract: f(A)b, the action of the function f of a matrix A on a vector b, is required in many applications, for example in exponential integrators, where f = exp or in lattice QCD where f(z) = z- α; α ϵ (0, 1). Typically, A is large and sparse, so computing f(A) directly is not possible, but subspace techniques allow to approximate f(A)b. In this talk will address issues related to the computation and to the
convergence analysis for Krylov subspace based methods. The outstanding problem in computation is how to obtain a stable restart procedure, and we show how this can be achieved when f can be adequately represented by a contour integral. On the analytical side, we present convergence results when f is a Stieltjes function and A is symmetric and positive de nite and, with appropriate modi cations, when A is just positive de nite but not necessarily symmetric. Finally, we will address generalizations to the block case, i.e. when several vectors b are to be treated simultaneously.
The presentation will take place in HS 9
We will meet over coffee in E10 at 15:45