计算机工程与应用 ›› 2008, Vol. 44 ›› Issue (3): 78-80.

• 学术探讨 • 上一篇    下一篇

基于LDLT分解求实对称矩阵特征值的递归算法

张 鹍1,张有志2   

  1. 1.山东大学 威海分校,山东 威海 264209
    2.山东大学 信息科学与工程学院,济南 250100
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2008-01-21 发布日期:2008-01-21
  • 通讯作者: 张 鹍

Recursive algorithm for calculating eigenvalues of real symmetric matrix based on LDLT decomposition

ZHANG Kun1,ZHANG You-zhi2   

  1. 1.Shandong University at Weihai,Weihai,Shandong 264209,China
    2.School of Inf. Sci. and Eng.,Shandong University,Ji’nan 250100,China
  • Received:1900-01-01 Revised:1900-01-01 Online:2008-01-21 Published:2008-01-21
  • Contact: ZHANG Kun

摘要: 基于线性代数与矩阵理论,给出利用LDLT分解计算实对称矩阵特征值的递归算法。该算法可求出实对称矩阵在给定区间内的特征值的个数,并可计算满足精度要求的特征值。理论分析和实际测试证明该算法是有效的。

关键词: LDLT分解, 实对称矩阵, 特征值, 递归算法

Abstract: A recursive algorithm for calculating the eigenvalues of a real symmetric matrix based on LDLT decomposition is given.With this algorithm,the number of eigenvalues of a real symmetric matrix in the given interval can be counted,and the eigenvalues of the matrix can be calculated.Through theoretical analysis and numerical simulation,this algorithm is proved to be effective.

Key words: LDLT decomposition, real symmetric matrix, eigenvalue, recursive algorithm