Summary: PROJECTED GMRES AND ITS VARIANTS
Br gida Molina
Centro de Calculo Cientfico y Tecnologico (CCCT),
Facultad de Ciencias, Universidad Central de Venezuela (UCV),
Ciudad Universitaria, Av. Los Estadios, Los Chaguaramos, CaracasVenezuela.
Abstract: In this work, we propose a new Krylov iterative method to solve systems of linear
equations. This method is a variant of the wellknown GMRES and is based on modifications over
the constraints imposed on the residual vector, i.e., this vector is projected in another subspace
and impose the constraints over this projection, because of this, we called the method: Projected
GMRES (PRGMRES). Additionally, we develope two versions of PRGMRES: the PRGMRES
with Biorthogonalization (BPRGMRES) and the Inexact PRGMRES (IPRGMRES). Experimental
results are presented to show the good performances of the new methods, compared to FOM(m)
Keywords: restarted GMRES, Krylov Subspace methods, PetrovGalerkin conditions, unsymmet
ric linear systems.
In a variety of engineering and scientific applications we need to solve different systems of differ