Convergence of the extrapolated aor and sor iterative methods

Abstract

In this paper we discuss the EAOR and the ESOR iterative methods to solve the linear system when its coefficient matrix is an L-matrix, an H-matrix, or strictly or irreducibly diagonally dominant, or when it belongs to the class C1 From our results receniven in [3,4] we give the Stein-Rosenberg type theorems and the upper bounds of the spectral radii of the EAOR and the ESOR iteraion matrices, establish the convergence domains of the EAOR and the ESOR methods, and extend the previous results [1]. Finally we give the sufficient and necessary conditions to determine a matrix to be an M-matrix, or an H-matrix, or strictly or irreducibly diagonally dominant.