CSE Seminar
Daniel Szyld, Temple University
DATE: Wednesday, September 3, 2003
TIME: 12:00 noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
TITLE: Convergence of Inexact Krylov Methods
Abstract
We provide a general framework for understanding inexact Krylov
subspace methods. In inexact methods, the matrix-vector product at
each step is not performed exactly. This framework allows us to
explain empirical results reported in the literature, where the
exactness of the matrix-vector product is allowed to deteriorate as the
Krylov subspace method progresses. A computable criterion is proposed
to bound the inexactness of the matrix-vector multiplication in such a
way as to maintain the convergence of the Krylov subspace method. The
theory developed is applied to several problems. Numerical experiments
are reported where the computable criteria are successfully applied.
Furthermore, a theory is presented explaining the superlinear
convergence of exact and inexact Krylov subspace methods.
This is joint work with Valeria Simoncini.