Convergence of Inexact Krylov Subspace Methods
 
Daniel B. Szyld
Temple University

Krylov subspace methods are possibly today's most widely
use iterative methods for the solution of linear systems
of algebraic equations in science and engineering.
We give a short introduction to these methods and then
provide a general framework for the understanding of
Inexact Krylov subspace methods.  In the inexact methods, 
the matrix-vector product at each step is not performed exactly.
This framework allows us to explain the 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.


Joint work with Valeria Simoncini