| 引用本文: | 罗晓广,李晓梅.求解对称三对角矩阵特征值问题的一种新算法.[J].国防科技大学学报,1997,19(3):44-49.[点击复制] |
| Luo Xiaoguang,Li Xiaomei.A New Algorithm for the Eigenvalue Problem of Symmetric Tridiagonal Matrices[J].Journal of National University of Defense Technology,1997,19(3):44-49[点击复制] |
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| 求解对称三对角矩阵特征值问题的一种新算法 |
| 罗晓广, 李晓梅 |
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(国防科技大学 计算机系 湖南 长沙 410073)
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| 摘要: |
| 关于对称三对角矩阵特征值问题, 本文提出一种新的分治算法。新算法以二分法、割线法迭代为基础。不同于Cuppen's 方法和Laguerre 迭代法。理论分析和数值实验的结果表明: 新算法的收敛速度明显比文[1]中的Laguerre 迭代法快。在相同的精度要求下, 当问题规模较大时, 使用新算法能减少40%以上的计算时间。 |
| 关键词: 特征值, 割线法, 二分法, Laguerre 迭代 |
| DOI： |
| 投稿日期：1996-12-20 |
| 基金项目:国防预研课题资助项目 |
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| A New Algorithm for the Eigenvalue Problem of Symmetric Tridiagonal Matrices |
| Luo Xiaoguang, Li Xiaomei |
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(Department of Computer, NUDT, Changsha, 410073)
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| Abstract: |
| This paper presents a new divide-and-conquer algorithm for the eigenvalue problem of symmetric tridiagonal matrices. The new algorithm oases on bisection and secant iteration, which is different from Cuppen's method and Laguerre iteration. The results of theoretical analysis and numerical testing show that the convergent rate of our algorithm is obviously faster than that of Laguerre iteration presented in [1]. When the problem scale is quite large, with the same requirement of accuracy, more than 40% of the computing time can be reduced by using this new algorithm. |
| Keywords: eigenvalues, secant method, bisection algorithm, Laguerre iteration |
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