The SOR-k Method for Linear Systems with P-Cyclic Matrices

Authors

Liancheng Wang, Kennesaw State UniversityFollow
Jiehua Zhu, Georgia Southern University
Xiezhang Li, Georgia Southern University

Department

Mathematics

Document Type

Article

Publication Date

7-2010

Abstract

Let the system matrix of a linear system be p-cyclic and consistently ordered. Under the assumption that the pth power of the associated Jacobi matrix has only non-positive eigenvalues, it is known that the optimal spectral radius of the SOR-k iteration matrix is strictly increasing as k increases from 2 to p. In this paper, we first show that the optimal parameter of the SOR-k method as a function of k is strictly increasing. The behaviour of the spectral radius of the SOR-k method (for fixed parameter) is then studied.