Sor method and P-cyclic matrices (II)

Abstract

In [1] we have shown that when the SOR method is used for solving the p-cyclic system (1.1) then partitioning the p-cyclic matrix A into 2-cyclic form results in a faster convergence rate

In this paper we want to show that partitioning the p-cyclic matrix A into 2-cyclic form is the best according to the spectral radius, or equivalently the asymptotic rate of convergence, even though many other choices are available for considering the p-cyclic matrix A as k-cyclic formsk=3,…,p.

Keywords:

• SOR method
• p-cyclic matrix and linear systems

SUBJECT CLASSIFICATION:

• 65F10

^∗Permanent address: Shenyang Institute of Computing Technology, Chinese Academy of Sciences, Shenyang, China.

^∗Permanent address: Shenyang Institute of Computing Technology, Chinese Academy of Sciences, Shenyang, China.

Notes

^∗Permanent address: Shenyang Institute of Computing Technology, Chinese Academy of Sciences, Shenyang, China.