# Computational Mathematics and Scientific Computing Seminar

## The Stability of GMRES Convergence, With Application to Preconditioning by Approximate Deflation

**Speaker:**
Josef Sifuentes, CIMS

**Location:**
Warren Weaver Hall 1302

**Date:**
Oct. 1, 2010, 10 a.m.

**Synopsis:**

How does GMRES convergence change when the coefficient matrix is perturbed? Through resolvent estimates we develop simple, general bounds to quantify the lag in convergence such a perturbation can induce. This analysis is particlarly relevant for preconditioned systems, where an ideal preconditioner is only approximately applied in practical computations. To illustrate the utility of this theory, we combine our analysis with Stewart's invariant subspace perturbation theory to develop rigorous bounds on the performance of approximate deflation preconditioning using Ritz vectors.