Computer Science NASC Seminar

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

Josef Sifuentes, CIMS

October 01, 2010 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110
(Directions)

Fall 2010 NASC Seminars Calendar

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.


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