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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)
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1975
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2016-04-27
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bwmeta1.element.ojs-doi-10_14708_ma_v3i5_1182