Convergence of Matrix Iterations Subject to Diagonal Dominance
Convergence of Matrix Iterations Subject to Diagonal Dominance
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DOI：
10.1137/0710042
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发表时间：
1973-06
影响因子：
2.9
通讯作者：
K. R. James
中科院分区：
文献类型：
--
作者：
K. R. James
研究了求解线性方程组的循环迭代法，给出了迭代收敛的充分必要条件。给出了严格不可约弱对角占优下点Gauss-Seidel迭代和Jacobi迭代收敛性的一种新的简洁证明方法。该方法的发展，以获得收敛条件，以前没有建立，平稳松弛过程的高斯-赛德尔和雅可比型。得到迭代矩阵的谱半径上的界，因此松弛参数的值的范围是足以保证收敛。
Cyclic iterative methods of solving systems of linear equations are investigated with reference to necessary and sufficient conditions for convergence. A new and concise method of proof is given for the convergence of point Gauss–Seidel and Jacobi iterations subject to strict and irreducible weak diagonal dominance. The method is developed to obtain convergence conditions, not previously established, for stationary relaxation processes of Gauss–Seidel and Jacobi type. Bounds are obtained on the spectral radius of the iteration matrix, hence a range of values of the relaxation parameter is derived sufficient to guarantee convergence.