On exact convergence of the accelerated overrelaxation method when applied to consistently ordered systems

Abstract

The problem of determining the exact regions of convergence and divergence of the block Accelerated Overrelaxation (AOR) iterative method, when it applies to systems with a Generalized Consistently Ordered (GCO) coefficient matrix, is addressed here. Some new algebraic results in the theory of regular splittings are obtained and used for the determination of extended regions of convergence. Complementary, in some cases, divergence regions are obtained by making use of a recently derived eigenvalue functional equation.

Keywords:

• Iterative methods
• accelerated overrelaxation
• generalized consistently ordered matrices
• regular splittings
• eigenvalues