International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 5, Pages 251-284
doi:10.1155/S0161171201007062
Matrix splitting principles
Zbigniew I. Wożnicki
Institute of Atomic Energy, Otwock-Świerk 05-400, Poland
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.