The Optimal Parameters of SOR-k Methods for P-Cyclic Matrices

Document Type

Article

Publication Date

4-1-2008

Publication Title

Applied Mathematics and Computation

DOI

10.1016/j.amc.2007.08.092

ISSN

0096-3003

Abstract

Consider a SOR-k method for solving a p -cyclic system Ax = b (p > 2) if the p -cyclic matrix A is repartitioned as a k -cyclic matrix for 2 ⩽ k ⩽ p . Suppose that the block Jacobi matrix B associated with A is convergent and all the eigenvalues of B p are nonnegative. A comparison of the optimal spectral radius of the SOR-k iteration matrix Lω(k) for 2 ⩽ k ⩽ p was given by Evan and Li under an assumption of the existence and differentiability of an implicit function. In this paper, the assumption is deleted. A comparison of the optimal parameter of SOR-k method, as k varies from 2 to p , is given. We will also compare the spectral radius of Lω(k) for a fixed ω and different values of k.

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