| 求解H-矩阵线性方程组的预处理Gauss-Seidel方法 |
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| 引用本文： | 邵新慧,沈海龙,张铁.求解H-矩阵线性方程组的预处理Gauss-Seidel方法[J].东北大学学报(自然科学版),2012,33(8):1213-1216. |
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| 作者姓名： | 邵新慧 沈海龙 张铁 |
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| 作者单位： | 1. 东北大学理学院,辽宁沈阳,110819
2. 东北大学理学院,辽宁沈阳110819 东北大学信息科学与工程学院,辽宁沈阳110819 |
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| 基金项目： | 国家自然科学基金资助项目，中央高校基本科研业务费专项资金资助项目 |
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| 摘 要： | 针对系数矩阵A为H-矩阵,为线性方程组Ax=b引入了两种形式的预处理矩阵I+-S和I+S^,给出了相应的预处理Gauss-Seidel方法.证明了若系数矩阵A为H-矩阵,则新的系数矩阵(I+-S)A和(I+S^)A仍是H-矩阵,并给出了相应预条件Gauss-Seidel方法的收敛性分析.通过数值算例验证了新的预处理迭代方法的收敛率比经典的Gauss-Seidel迭代法以及J.P.Milaszewicz提出的改进Gauss-Seidel迭代法更好.
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| 关 键 词： | H-矩阵 线性方程组 Gauss-Seidel方法 预处理矩阵 收敛率 |
Preconditioning Gauss-Seidel Methods for the Solution of H-Matrices Systems |
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| SHAO Xin-hui,SHEN Hai-long,ZHANG Tie.Preconditioning Gauss-Seidel Methods for the Solution of H-Matrices Systems[J].Journal of Northeastern University(Natural Science),2012,33(8):1213-1216. |
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| Authors: | SHAO Xin-hui SHEN Hai-long ZHANG Tie |
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| Institution: | 1(1.School of Sciences,Northeastern University,Shenyang 110819,China;2.School of Information Science & Engineering,Northeastern University,Shenyang 110819,China) |
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| Abstract: | For the linear equations Ax=b,two new preconditioning matrices I+ and I+ were introduced,and corresponding Gauss-Seidel methods were obtained.It was proved that if the coefficient matrix A of the original system was an H-matrix,then the coefficient matrices(I+)A and(I+) A of the preconditioning system were also an H-matrix.The convergence theorems of the new methods were proposed.Finally,numerical example was carried out and the results indicated that the convergence rates of the new preconditioning methods are better than those of the corresponding classical Gauss-Seidel method and the modified Gauss-Seidel method proposed by J.P.Milaszewicz. |
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| Keywords: | H-matrix linear equations Gauss-Seidel method preconditioning matrix convergence rate |
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