Title

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

Document Type

Article

Publication Date

2010

Publication Title

International Journal of Computer Mathematics

DOI

10.1080/00207160802464605

ISSN

1029-0265

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.

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