Jasper van den Eshof : November 13, 2002

Inexact Krylov subspace methods for linear systems: analysis and practice.

Abstract

There is a class of linear problems for which a matrix-vector product is very time consuming to compute since an expensive approximation method isnecessary to compute it with some prescribed relative precision.

In this talk we discuss analysis of the effects of approximate matrix-vector products on various Krylov subspace methods. This leads to strategies for picking the precision of the matrix-vector products that try to allow the ``error'' in the matrix-vector product to be as large as possible without compromising the convergence speed and accuracy too much. Our analysis confirms the ``relaxation'' strategies proposed in a series of Cerfacs reports.

Furthermore, we discuss some ideas about effectively applying these type of strategies in practical situations.