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

Authors

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

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.

Recommended Citation

Wang, Liancheng, Jiehua Zhu, Xiezhang Li. 2010. "The SOR-k Method for Linear System with P-Cyclic Matrices." International Journal of Computer Mathematics, 87 (8): 1785-1794. doi: 10.1080/00207160802464605
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/91