Inexact range-space Krylov solvers for linear systems 
                   arising from inverse problems 

             S. Gratton  Ph. L. Toint  J. Tshimanga Ilunga

             Report TR09/20         December 2009

The object of this paper is twofold. Firstly, range-space variants of standard
Krylov iterative solvers are introduced for unsymmetric and symmetric linear
systems.  These are characterized by possibly much lower storage and
computational costs than their full-space counterparts, which is crucial in
data assimilation applications and other inverse problems. Secondly, it is
shown that the computational cost may be further reduced by using inexact
matrix-vector products: formal error bounds are derived on the size of the
residuals obtained under two different accuracy models, and it is shown why a
model controlling forward error on the product result is often preferable to
one controlling backward error on the operator.  Numerical examples
finally illustrate the developed concepts and methods.