Matrix splitting principles

Abstract

The systematic analysis of convergence conditions, used in comparison theorems proven for different matrix splittings, is presented. The central idea of this analysis is the scheme of condition implications derived from the properties of regular splittings of a monotone matrix A = M 1 − N 1 = M 2 − N 2 . An equivalence of some conditions as well as an autonomous character of the conditions and A −1 N 2 ≥ A −1 N 1 ≥ 0 are pointed out. The secondary goal is to discuss some essential topics related with existing comparison theorems.