|本期目录/Table of Contents|

三对角与五对角Toeplitz 矩阵求逆的算法(PDF)

《纯粹数学与应用数学》[ISSN:1008-5513/CN:61-1240/O1]

期数:
2010年02期
页码:
292-299
栏目:
出版日期:
2010-04-25

文章信息/Info

Title:
An algorithm for the inverse of tri-diagonal and ˉve-diagonal Toeplitz matrices
作者:
刘刚 黄廷祝
(电子科技大学应用数学学院, 四川成都610054)
Author(s):
LIU Gang HUANG Ting-zhu
(School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China)
关键词:
Toeplitz 矩阵 三对角矩阵 五对角矩阵 循环矩阵
Keywords:
Toeplitz matrix ˉve-diagonal matrix tri-diagonal matrix circulant matrix
分类号:
O241.6
DOI:
-
文献标识码:
A
摘要:
提出了一种求三对角与五对角Toeplitz 矩阵逆的快速算法, 其思想为先 将Toeplitz 矩阵扩展为循环矩阵, 再快速求循环矩阵的逆, 进而运用恰当矩阵分块求 原Toeplitz 矩阵的逆的算法. 算法稳定性较好且复杂度较低. 数值例子显示了算法的有 效性和稳定性, 并指出了算法的适用范围.
Abstract:
This paper introduces a new algorithm for the inverse of tri-diagonal and ˉve-diagonal Toeplitz matrix. Its main idea is expanding the Toeplitz matrix to a circulant matrix ˉrst and then computing the inverse of the new circulant matrix, and ˉnally computing the inverse of the former Toeplitz matrix with appropriate matrix spit. The algorithm has little better stability and little cost. Numerical examples illustrate the e?ectivity and stability of the algorithm, and indicate the scope of application of the algorithm.

参考文献/References

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备注/Memo

备注/Memo:
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更新日期/Last Update: 2010-06-02