Error Bounds for some overrelaxation methods

Abstract

Suppose Ax = b is a system of linear equations where the matrix A is symmetric positive definite and consistently ordered. Some bounds for ∥ε _k :∥2 in terms of the norms of and and their inner product for the SOR, SSOR, USSOR, MSOR and AOR methods have been given by many authors. Recently, Li presents a uniform bound for the overrelaxation methods. In this paper, an error bound for the USMAOR method is derived. As special cases of the USMAOR method, bounds of ∥ε _k :∥2 for the SMAOR, USMSOR, SMSOR, USAOR, SAOR, USSOR, SSOR, MAOR, MSOR, AOR, EAOR, EGS I, EGS II, SOR, JOR, Gauss-Seidel and Jacobi methods are obtained

Keywords:

• Linear systems
• overrelaxation methods
• error bound

AMS(MOS) Subject Classification::

• 65F10

C.R. Categories::

• G.1.3