International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 5, Pages 251-284
doi:10.1155/S0161171201007062
Matrix splitting principles
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.
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=M1−N1=M2−N2. An
equivalence of some conditions as well as an autonomous character
of the conditions M1−1≥M2−1≥0 and A−1N2≥A−1N1≥0 are pointed out. The
secondary goal is to discuss some essential topics related with
existing comparison theorems.