用割线法迭代求解对称三对角矩阵特征值问题

为对称三对角矩阵特征值问题，提出一种新的分而治之的算法。新算法以二分法，割线法迭代为基础，不同于Ｃｕｐｐｅｎ的方法和Ｌａｎｇｕｅｒｒｅ迭代法。理论分析和数据实验的结果表明：新算法的收敛速度明显比文［１］中的Ｌａｇｕｅｒｒｅ迭代法快。

Solving the Eigenvalue Problem of Symmetric Tridiagonal Matrices by Secant Iteration

This paper presents a new divide-and-conquer algorithm for the eigenvalue problem of symmetric tridiagonal matrices. The new algorithm bases 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 convergence rate of our algorithm is obviously faster than that of Laguerre iteration presented in . When the problem scale is quite large, more than 40% of the computing time can be saved by using this new algorithm with the same requirement of accuracy.