A stable Richardson iteration method for complex linear systems

The Richardson iteration method is conceptually simple, as well as easy to program and parallelize. This makes the method attractive for the solution of large linear systems of algebraic equations with matrices with complex eigenvalues. We change the ordering of the relaxation parameters of a Richardson iteration method proposed by Eiermann, Niethammer and Varga for the solution of such problems. The new method obtained is shown to be stable and to have better convergence properties.