On estimating the largest eigenvalue with the Lanczos algorithm
On estimating the largest eigenvalue with the Lanczos algorithm
复制标题
用Lanczos算法估计最大特征值
DOI：
10.1090/s0025-5718-1982-0637293-9
复制
发表时间：
1982
影响因子：
2
通讯作者：
L. Stringer
中科院分区：
文献类型：
--
作者：
B. Parlett;H. Simon;L. Stringer
应用于正定矩阵的Lanczos算法在几次迭代之后产生对谱的极端端的特征值的良好近似。在本文中，我们利用这种行为，并开发了一个简单的算法，计算最大的特征值。该算法在矩阵阶数较大且精度要求较低的情况下尤其经济。讨论了失聚现象。文中还给出了该算法的一些简单推广.最后给出了一些数值例子并与幂方法进行了比较。
The Lanczos algorithm applied to a positive definite matrix produces good approximations to the eigenvalues at the extreme ends of the spectrum after a few iterations. In this note we utilize this behavior and develop a simple algorithm which computes the largest eigenvalue. The algorithm is especially economical if the order of the matrix is large and the accuracy requirements are low. The phenomenon of misconvergence is discussed. Some simple extensions of the algorithm are also indicated. Finally, some numerical examples and a comparison with the power method are given.