Another Step Toward an Optimal Two-Parameter SOR Method

Abstract

The SOR method is a well-known method obtained from a one-part splitting of the system matrix $A$, using one parameter $\omega$ for the diagonal. Using one parameter for the lower triangular matrix of $A$, M. Sisler introduced a new method. Later, he combined the standard SOR method and his method to get a two-parameter method. Sisler proved that for cyclic and positive-definite matrices, if zero is an eigenvalue of the Jacobi iteration matrix, the two-parameter method is not superior to the SOR method. In this paper we generalize Sisler's method and provide a range for the second parameter on which the two-parameter method is superior to the SOR method.