| 一类预条件矩阵USSOR迭代方法的比较定理 |
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| 引用本文： | 郭煜,畅大为. 一类预条件矩阵USSOR迭代方法的比较定理[J]. 纺织高校基础科学学报, 2011, 0(4): 546-548 |
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| 作者姓名： | 郭煜 畅大为 |
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| 作者单位： | 陕西师范大学数学与信息科学学院;陕西邮电职业技术学院基础部 |
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| 基金项目： | 国家自然科学基金资助项目(60671063) |
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| 摘 要： | 为了提高线性方程组迭代法的收敛速度,采用适当的预处理方法是必要的,即PAx=Pb.利用新预条件矩阵P=I+C′α,当系数矩阵A为非奇异M-矩阵时,运用USSOR迭代方法及矩阵分裂理论,获得了新的比较定理.最后通过数值例子验证了所得的主要结论.
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| 关 键 词： | 比较定理 矩阵分裂 谱半径 预条件 USSOR迭代方法 |
Convergence theorems for USSOR iterative method with some preconditioned matrices |
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| GUO Yu,CHANG Da-wei. Convergence theorems for USSOR iterative method with some preconditioned matrices[J]. Basic Sciences Journal of Textile Universities, 2011, 0(4): 546-548 |
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| Authors: | GUO Yu CHANG Da-wei |
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| Affiliation: | 1 (1.College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China; 2.Department of Basic Courses,Shaanxi Post and Telecommunication College,Xianyang,Shaanxi 712000,China) |
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| Abstract: | In order to improve the convergence rate of linear equations iterative method,using the appropriate pretreatment is necessary,that is the case PAx=Pb.The new preconditioned matrices P=I+C′α was used.When the coefficient matrix A is nonsingular M-matrix,using the USSOR iterative methods and the theory of matrix splitting,the comparison theorem is obtained.Finally,the main result is demonstrated by a numerical example. |
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| Keywords: | comparison theorems the theory of matrix splitting spectral radius preconditioned USSOR iterative method |
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