| Toeplitz系数矩阵方程组的迭代解法 |
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| 引用本文： | 方雅敏.Toeplitz系数矩阵方程组的迭代解法[J].丽水学院学报,2008,30(2):25-28. |
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| 作者姓名： | 方雅敏 |
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| 作者单位： | 丽水学院,数理学院,浙江,丽水,323000 |
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| 摘 要： | 主要讨论系数矩阵为非对称正定的Toeplitz的迭代求解，运用以系数矩阵的一个对称、反对称分裂为基础的SSS迭代方法。特别地分裂是一个中心对称分裂，可以利用中心对称矩阵的可约性来减少计算量和存储量。再通过几个数值例子验证了此方法的有效性。
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| 关 键 词： | Toeplitz矩阵 迭代方法 矩阵分裂 谱半径 中心对称矩阵 |
| 文章编号： | 1008-6749(2008)02-0025-04 |
| 修稿时间： | 2008年1月26日 |
The Iterative Method for the Linear Systems with Toeplitz Matrices |
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| Fang Yamin.The Iterative Method for the Linear Systems with Toeplitz Matrices[J].Journal of Lishui University,2008,30(2):25-28. |
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| Authors: | Fang Yamin |
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| Institution: | Fang Yamin (College of Mathematics and Physics,Lishui University,Lishui Zhejiang 323000,China) |
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| Abstract: | In this paper,we investigated a new iterative method for the linear system with a non-symmetric positive definite Toeplitz matrix,which is called the SSS iterative method.The SSS iterative method is based on a symmetric and skew-symmetric matrix splitting of A,in particular,the splitting is a centrosymmetric splitting,so we can reduce the computation and store cost of the SSS iterative method by the centrosymmetric property.Finally we test the effectiveness of the SSS iterative method by several numerical examples. |
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| Keywords: | Toeplitz matrix iterative method matrix splitting spectral radius centrosymmetric matrices |
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