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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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 |
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doaj-9bf490da201b4a46a8b7a4d1d07d82352020-11-24T22:35:07ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0128525128410.1155/S0161171201007062Matrix splitting principlesZbigniew I. Woźnicki0Institute of Atomic Energy, Otwock–Świerk 05–400, PolandThe 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.http://dx.doi.org/10.1155/S0161171201007062 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zbigniew I. Woźnicki |
| spellingShingle |
Zbigniew I. Woźnicki Matrix splitting principles International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Zbigniew I. Woźnicki |
| author_sort |
Zbigniew I. Woźnicki |
| title |
Matrix splitting principles |
| title_short |
Matrix splitting principles |
| title_full |
Matrix splitting principles |
| title_fullStr |
Matrix splitting principles |
| title_full_unstemmed |
Matrix splitting principles |
| title_sort |
matrix splitting principles |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2001-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S0161171201007062 |
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AT zbigniewiwoznicki matrixsplittingprinciples |
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