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求解周期三对角Toeplitz方程组的一种新修正算法

徐仲,安晓虹,陆全   

  1. 西北工业大学应用数学系, 西安 710072
  • 出版日期:2008-12-14 发布日期:2008-12-24
  • 基金资助:

    国家自然科学基金项目 (10802068), 陕西省自然科学基金项目 (2006A05) 资助.

徐仲,安晓虹,陆全. 求解周期三对角Toeplitz方程组的一种新修正算法[J]. 数值计算与计算机应用, 2008, 29(4): 291-295.

Xu Zhong, An Xiaohong, Lu Quan. A NEW MODIFIED ALGORITHM FOR SOLVING PERIODIC TRIDIAGONAL TOEPLITZ SYSTEMS[J]. Journal of Numerical Methods and Computer Applications, 2008, 29(4): 291-295.

A NEW MODIFIED ALGORITHM FOR SOLVING PERIODIC TRIDIAGONAL TOEPLITZ SYSTEMS

Xu Zhong, An Xiaohong, Lu Quan   

  1. Department of Mathematics, Northwestern Polytechnical University,   Xi'an 710072, China
  • Online:2008-12-14 Published:2008-12-24

利用Sherman-Morrison-Woodbury公式导出了求解周期三对角Toeplitz方程组的一 种新的修正算法.该算法的计算量比求解周期三对角方程组的追赶法要少,且可以 并行计算.对新算法进行了可行性和稳定性分析.数值算例表明了新算法的有效性

In this paper, a new modified algorithm for solving periodic tridiagonal Toeplitz systems is presented by using the Sherman-Morrison-Woodbury formula. The algorithm has less computational cost than the Thomas algorithm for solving periodic tridiagonal systems. Moreover, parallel
computations can be implemented in the algorithm. The feasibility and stability of the algorithms are analyzed. Numerical examples illustrate
the effectiveness of the algorithm.

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[1]徐仲, 张凯院, 陆全. Toeplitz矩阵类的快速算法[M]. 西安: 西北工业大学出版社. 1999.
[2]D. J. Evans. On the solution of certain Toeplitz tridiagonal linear systems[J]. SIAM J. Numer. Anal., 1980, 17: 675-680
[3]陈明逵. 解特殊三对角线性方程组的修正追赶法[J]. 西安交通大学学报, 1982, 16(5): 85-94.
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