A note on weighted FOM and GMRES for solving nonsymmetric linear systems

摘要

Recently Essai [Numer. Algorithm 18 (1998) 277–292] presented two new methods called WFOM and WGMRES for solving nonsymmetric linear systems. In this note we first point out a scaling invariant property of these methods, then we discuss the performance of the preconditioned weighted FOM and GMRES. Experimental results are presented to show that, contrast to WFOM and WGMRES, the preconditioned weighed FOM and GMRES have not so good performance compared to preconditioned FOM(m) and preconditioned GMRES(m).