Optimum sor convergence for complex spectra

Abstract

In this paper it is assumed that the point (or block) Jacobi matrix J _k associated with the matrix A is weakly k-cyclic consistently ordered with complex, in general, eigenvalue spectrum σ

(J _k ). It is then our objective to begin a study in order to extend the Young-Eidson algorithm for the determination of the real optimum relaxation factor in the monoparametric k-step iterative method or equivalently in the case of the Successive Overelaxation (SOR-k) method when σ(J _k ) lies in a cusped hypocycloid region. In addition a number of concluding remarks are made and numerical examples are given, that support the theory developed in this paper.

Keywords:

• SOR-k method
• k-step iterative method
• k-cyclic matrix and complex spectra

C.R. Categories:

• G.1.3