Kirk M. Soodhalter,
"Two recursive GMRES-type methods for shifted linear systems with general preconditioning"
, in arXiv/Review by journal, 6-2014
Two recursive GMRES-type methods for shifted linear systems with general preconditioning
Sprache des Titels:
We present two minimum residual methods for solving sequences of shifted
linear systems, the right-preconditioned shifted GMRES and shifted
Recycled GMRES algorithms. These methods are compatible with general
preconditioning of all systems, and when restricted to right preconditioning,
require no extra applications of the operator or preconditioner.
These methods perform a minimum residual iteration for the base system
while improving the approximations for the shifted systems at little
additional cost. The iteration continues until the base system approximation
is of satisfactory quality. The method is then recursively called
for the remaining unconverged systems. We present both methods inside
of a general framework which allows these techniques to be extended
to the setting of flexible preconditioning and inexact Krylov methods.
We present some analysis of such methods and numerical experiments
demonstrating the effectiveness of the algorithms we have derived.