A New Version for Simpler GMRES

GMRES is an iterative method that provides better solutions when dealing with larg linear systems of equations with unsymmetric coefficient matrix. By shifting the Arnoldi process to begin with Ar0 instead of r0, simpler GMRES implementation, proposed by Walker and Zhou in 1994, is obtained that in this method, an upper triangular problem is solved instead of hessenberg least square problem. This method is mathematically equivalent to the standard GMRES. In this paper, we apply weighted Arnoldi process on simpler GMRES to accelerate the convergence of this method. Numerical results show that this technique is applicable for simpler GMRES.