A convergence analysis of SOR iterative methods for linear systems with weak H-matrices

Abstract

It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.

Keywords

• convergence
• weak h-matrices
• nonstricly diagonally dominant matrices
• diagonally dominant matrices
• diagonally equipotent matrices
• sor iterative methods
• 15a06
• 15a18
• 15a42