一种求解大型稀疏对称矩阵(极端)特征值问题的有效算法

计算物理 ›› 1996, Vol. 13 ›› Issue (3): 359-365.

一种求解大型稀疏对称矩阵(极端)特征值问题的有效算法

杜玉越

聊城师范学院计算中心, 山东聊城 252059

收稿日期:1995-01-02 出版日期:1996-09-25 发布日期:1996-09-25

AN EFFECTIVE ALGORITHM FOR SOLVING (THE LARGEST OR LOWEST) EIGENPROBLEMS OF LARGE SPARSE SYMMETRIC MATRICES

Du Yuyue

Computing Center, Liaocheng Teachers College, Shandong Liaocheng 252059

Received:1995-01-02 Online:1996-09-25 Published:1996-09-25

摘要/Abstract

摘要： 提出一种求解大型稀疏对称矩阵几个最大(最小)特征值和相应特征向量的迭代块DL(即Davidson-Lanczos)算法并且讨论了迭代块DL算法的收敛率

关键词: 对称矩阵, 特征值和特征向量, DL算法, 迭代块DL算法

Abstract: An iterative block DL (i.e. Davidson-Lanczos) algorithm is presented for computing a few of the largest (or lowest) eigenvalues and corresponding eigenvectors of very large sparse symmetric matrices. It's convergence rate is also discussed. it overcomes the disadvantages of the DL method which cann't find multiple or clustered eigenvalues, and the convergence speed of the mesent method is far faster than the DL method. Numerical results are compared whith those by the DL algorithm in a few experiments which exhibit a sharp-superiority of the new approach.

Key words: Symmetric matrix, eigenvalue and eigenvector, DL algorithm, iterative block DL algorithm

中图分类号:

O241

杜玉越. 一种求解大型稀疏对称矩阵(极端)特征值问题的有效算法[J]. 计算物理, 1996, 13(3): 359-365.

Du Yuyue. AN EFFECTIVE ALGORITHM FOR SOLVING (THE LARGEST OR LOWEST) EIGENPROBLEMS OF LARGE SPARSE SYMMETRIC MATRICES[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 13(3): 359-365.