Summary: PROJECTED GMRES AND ITS VARIANTS
Reinaldo Astudillo
Br� �gida Molina
rastudillo@kuaimare.ciens.ucv.ve
bmolina@kuaimare.ciens.ucv.ve
Centro de C�alculo Cient��fico y Tecnol�ogico (CCCT),
Facultad de Ciencias, Universidad Central de Venezuela (UCV),
Ciudad Universitaria, Av. Los Estadios, Los Chaguaramos, Caracas�Venezuela.
Abstract: In this work, we propose a new Krylov iterative method to solve systems of linear
equations. This method is a variant of the well�known 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)
and GMRES(m).
Keywords: restarted GMRES, Krylov Subspace methods, Petrov�Galerkin conditions, unsymmet�
ric linear systems.
1. INTRODUCTION
In a variety of engineering and scientific applications we need to solve different systems of differ�

Source: Astudillo, Reinaldo - Departamento de Computaci�n, Universidad Central de Venezuela

Collections: Computer Technologies and Information Sciences