Geodesic
Some sufficient conditions for the convergence of the Jacobi and Gauss-Seidel methods for large systems of linear equations
Mathematica Applicanda, Tome 3 (1975) no. 5, pp. 43-50.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

This article contains three sufficient conditions for the convergence of Jacobi and Gauss-Seidel iterative solutions of systems of linear equations of the form Ax=b. These conditions rely on a special property of the matrix A defined in this work as `the sum criterion'. This property is not equivalent in the general case to the irreducibility of the matrix A. The results obtained are regarded primarily as a theoretical aid towards understanding the Gauss-Seidel method. Practical usefulness of these methods is minimal since generally we can list other more effective iterative methods. (MR0455316)
DOI : 10.14708/ma.v3i5.1182
Mots-clés : 65F10 
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     title = {Some sufficient conditions for the convergence of the {Jacobi} and {Gauss-Seidel} methods for large systems of linear equations},
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Hò Thuân. Some sufficient conditions for the convergence of the Jacobi and Gauss-Seidel methods for large systems of linear equations. Mathematica Applicanda, Tome 3 (1975) no. 5, pp.  43-50. doi : 10.14708/ma.v3i5.1182. http://geodesic.mathdoc.fr/articles/10.14708/ma.v3i5.1182/

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