#### Title

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*.

#### Recommended Citation

Li, Xiezhang.
2008.
"The Optimal Parameters of SOR-*k* Methods for P-Cyclic Matrices."
*Applied Mathematics and Computation*, 197 (2): 614-621.
doi: 10.1016/j.amc.2007.08.092

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/94