Generalized line criterion for Gauss-Seidel method
We present a module based criterion, i.e. a sufficient condition based on the absolute value of the matrix coefficients, for the convergence of Gauss-Seidel method (GSM) for a square system of linear algebraic equations, the Generalized Line Criterion (GLC). We prove GLC to be the ''most general'' module based criterion and derive, as GLC corollaries, some previously know and also some new criteria for GSM convergence. Although far more general than the previously known results, the proof of GLC is simpler. The results used here are related to recent research in stability of dynamical systems and control of manufacturing systems.
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| Main Authors: | , , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática Aplicada e Computacional
2003
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| Online Access: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100006 |
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| Summary: | We present a module based criterion, i.e. a sufficient condition based on the absolute value of the matrix coefficients, for the convergence of Gauss-Seidel method (GSM) for a square system of linear algebraic equations, the Generalized Line Criterion (GLC). We prove GLC to be the ''most general'' module based criterion and derive, as GLC corollaries, some previously know and also some new criteria for GSM convergence. Although far more general than the previously known results, the proof of GLC is simpler. The results used here are related to recent research in stability of dynamical systems and control of manufacturing systems. |
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