GAOR迭代法的收敛性 |
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引用本文: | 宋永忠. GAOR迭代法的收敛性[J]. 计算数学, 1989, 11(4): 405-412 |
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作者姓名: | 宋永忠 |
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作者单位: | 南京师范大学 |
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摘 要: | 当A为实对称矩阵时,[1]中在D_i选取较特殊的条件下,证明了GAOR迭代法收敛的充要条件为A是正定矩阵. 设A为Hermite矩阵,进一步讨论GAOR迭代法收敛的充要条件. 以下记 B=D_1~(-1)(C_L+C_U).
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关 键 词: | GAOR迭代法 收敛性 线性方程组 |
ON THE CONVERGENCE OF GAOR METHODS |
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Affiliation: | Song Yong-zhong Department of Mathematics. Nanjing Normal University |
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Abstract: | In [1] the generalized accelerated overrelaxation (GAOR) methods were proposed, whichgeneralized the basic iterative methods for the solution of linear systems. This paper investiga-tes the convergence of the GAOR methods. A number of new results are presented concern-ing the convergence theory of the GAOR methods and their special cases. Much attention isgiven to linear systems whose coefficient matrices are positive definite, and are L-matrices andH-matrices, respectively. |
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