| Abstract: | This paper presents two new methods called WFOM and WGMRES, which are variants of FOM and GMRES, for solving large and sparse
nonsymmetric linear systems. To accelerate the convergence, these new methods use a different inner product instead of the
Euclidean one. Furthermore, at each restart, a different inner product is chosen. The weighted Arnoldi process is introduced
for implementing these methods. After describing the weighted methods, we give the relations that link them to FOM and GMRES.
Experimental results are presented to show the good performances of the new methods compared to FOM(m) and GMRES(m).
This revised version was published online in August 2006 with corrections to the Cover Date. |
