A note on weighted FOM and GMRES for solving nonsymmetric linear systems (Q1827017)

Recently \textit{A. Essai} [Numer. Algorithms 18, 277--292 (1998; Zbl 0926.65036)] presented two new methods called weighted full orthogonal method (WFOM) and weighted generalized minimal residual (WGMRES) method for solving nonsymmetric linear systems. In this note the authors first point out a scaling invariant property of these methods, then they discuss the performance of the preconditioned weighted FOM and GMRES. Experimental results are presented to show that, in 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).