A comparison of some GMRES-like methods

GMRES and cc,s arc well known iterative methods for the solution of certain sparse linear systems with a nonsymmetric matrix. These methods have been compared experimentally in many studies, and specific observations on their convergence behavior have been reported. A new iterative method to solve a nonsymmetric system has been proposed by Eirola and Nevanlinna. The purpose of this paper is to investigate this method and to compare it with GMRES. We have seen problems for which this method is more efficient than GMRES. The original method has as drawbacks that it is not scaling invariant and that it may suffer from numerical instability, but it is shown that these deficiencies can be repaired. A method proposed by Broyden (1969) seems related to the new method and is therefore included in the comparison