Mathematics Graduate Students Organization

Seminar:

Date: February 5

G. Petrova: "Greedy strategies for convex optimization"

Abstract: We investigate two greedy strategies for finding an approximation to the minimum of a convex function E defined on a Hilbert space H. We prove convergence rates for these algorithms under suitable conditions on the objective function E. These conditions involve the behavior of the modulus of smoothness and the modulus of uniform convexity of E.

W. Bangerth: "About some problems solving linear systems arising from flow problems"

Abstract: When one wants to solve flow problems on a computer, the first step is to "discretize" the partial differential equation that describes the flow to obtain a finite dimensional approximation. This typically requires the solution of a linear or nonlinear system of equation (and in the latter case, a Newton iteration will reduce it to a sequence of linear systems). Even for complex flow problems, this step is often well understood. However, one is then stuck with a (possibly very large) linear system. I will talk about some of the challenges that arise from solving it in practical contexts. I'll try to keep it at a level appropriate for first year graduate students from across the mathematical subdisciplines.