Matrix splitting principles
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 equi...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201007062 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |