| 关于Toeplitz+Hankel线性方程组的迭代解法 |
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| 引用本文： | 刘晓玲,刘仲云. 关于Toeplitz+Hankel线性方程组的迭代解法[J]. 数学理论与应用, 2014, 0(1): 7-11 |
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| 作者姓名： | 刘晓玲 刘仲云 |
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| 作者单位： | 长沙理工大学数学与计算科学学院,长沙410004 |
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| 基金项目： | 国家自然科学基金项目资助,基金号：11371075 |
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| 摘 要： | 本文研究Toeplitz+Hankel线性方程组的预处理迭代解法.我们提出了几个新的预条件子,并分析了预处理矩阵的谱性质,当生成函数在Wiener类中时,预处理矩阵的特征值聚集在1附近.数值实验表明该预处理子比文[5]中的预处理子更有效.
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| 关 键 词： | Toeplitz+Hankel 矩阵 预处理迭代法 Strang循环预处理子 T.Chan循环预处理子 |
The Iterative Methods to the Toeplitz- plus- Hankel Systems |
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| Liu Xiaoling School of Mathematics and Computing Science,Liu Zhongyun. The Iterative Methods to the Toeplitz- plus- Hankel Systems[J]. Mathematical Theory and Applications, 2014, 0(1): 7-11 |
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| Authors: | Liu Xiaoling School of Mathematics Computing Science Liu Zhongyun |
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| Affiliation: | Changsha University of Science and Technology, Changsha 410004, China) |
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| Abstract: | In this paper some preconditioned iterative methods for solving the Toeplitz - plus - Hankel systems are considered. Several new preconditioners for such kind of linear systems are proposed, and the spectral properties of preconditioned matrices are discussed. It is showed that the eigenvalues of the preconditioned matrices are clustered around the unity if the generating functions are in Wiener class. The Numerical experiments demonstrate that our pre- conditioners are more effective than those proposed in[2]. |
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| Keywords: | Toeplitz - plus - Hankel systems Preconditioned iterative method （PCG） Strang＇ s circulant pre-conditioner T. Chan＇s circulant preconditioner |
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