The SOR-k method for linear systems with p-cyclic matrices

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.

Keywords:

• linear system
• SOR method
• p-cyclic matrix

AMS Subject Classification :

• 65F10
• CR: 1.3

Acknowledgements

The authors sincerely thank the referees for their valuable comments and suggestions.