| 指数为1的半正定线性系统迭代方法的收敛性 |
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| 引用本文： | 崔艳星,王川龙.指数为1的半正定线性系统迭代方法的收敛性[J].太原师范学院学报(自然科学版),2013(1):32-34,39. |
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| 作者姓名： | 崔艳星 王川龙 |
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| 作者单位： | 长治学院数学系;太原师范学院数学系 |
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| 摘 要： | 当相容奇异线性系统系数矩阵的指数为1时，文章利用群逆的概念来介绍广义固定迭代方法半范数收敛，商收敛和收敛三者之间的关系，然后再利用群逆的概念来研究广义固定迭代方法半范数收敛的新条件．在保证迭代格式收敛的前提下，该条件比Keller的P-正则条件要弱．
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| 关 键 词： | 迭代格式 群逆 半范数收敛 商收敛 半正定线性系统 |
On the Convergence of Iterative Methods for Semi-Definite Linear Systems with Index One |
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| Cui Yanxing Wang Chuanlong.On the Convergence of Iterative Methods for Semi-Definite Linear Systems with Index One[J].Journal of Taiyuan Normal University:Natural Science Edition,2013(1):32-34,39. |
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| Authors: | Cui Yanxing Wang Chuanlong |
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| Institution: | Cui Yanxing Wang Chuanlong(1.Department of Mathematics,Changzhi University,Changzhi 046011;2.Taiyuan Normal University,Taiyuan 030012,China) |
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| Abstract: | We first use the group inverse to characterize the semi-norm convergence and quotient convergence the connection and distinction of stationary iterative schemes for solving consistent singular linear systems when the index of the coefficient matrix equals one. Then the new semi-norm convergent conditions of generalized iteration method are presented by using group inverse. The convergence of iterative schemes in ensuring the premise, this condition is wea- ker than Keller＇s P-regular conditions. |
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| Keywords: | iterative scheme group inverse semi-norm convergence quotient convergence semi-definite linear systems |
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