International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 5, Pages 251-284

Matrix splitting principles

Zbigniew I. Woźnicki

Institute of Atomic Energy, Otwock–Świerk 05–400, Poland

Received 15 March 2001

Copyright © 2001 Zbigniew I. Woźnicki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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=M1N1=M2N2. An equivalence of some conditions as well as an autonomous character of the conditions M11M210 and A1N2A1N10 are pointed out. The secondary goal is to discuss some essential topics related with existing comparison theorems.