On the convergence of the symmetric successive overrelaxation method

The symmetric successive overrelaxation (SSOR) iterative method is applied to the solution of the system of linear equations $\text{A}\text{x}\text{=}\text{b}$, where A is an n×n nonsingular matrix. We give bounds for the spectral radius of the SSOR iterative matrix when A is an Hermitian positive definite matrix, and when A is a nonsingular M-matrix. Then, we discuss the convergence of the SSOR iterative method associated with a new splitting of the matrix A which extends the results of Varga and Buoni [1].