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

Computer Engineering and Applications ›› 2008, Vol. 44 ›› Issue (3): 78-80.

• 学术探讨 • Previous Articles Next Articles

Recursive algorithm for calculating eigenvalues of real symmetric matrix based on LDL^T decomposition

ZHANG Kun¹,ZHANG You-zhi²

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

基于LDL^T分解求实对称矩阵特征值的递归算法

张鹍¹,张有志²

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

通讯作者: 张鹍

Abstract

Abstract: A recursive algorithm for calculating the eigenvalues of a real symmetric matrix based on LDL^T 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: LDL^T decomposition, real symmetric matrix, eigenvalue, recursive algorithm

摘要： 基于线性代数与矩阵理论，给出利用LDL^T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: LDL^T分解, 实对称矩阵, 特征值, 递归算法

ZHANG Kun¹,ZHANG You-zhi². Recursive algorithm for calculating eigenvalues of real symmetric matrix based on LDL^T decomposition[J]. Computer Engineering and Applications, 2008, 44(3): 78-80.

张鹍¹,张有志². 基于LDL^T分解求实对称矩阵特征值的递归算法[J]. 计算机工程与应用, 2008, 44(3): 78-80.

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Recursive algorithm for calculating eigenvalues of real symmetric matrix based on LDL^T decomposition

基于LDL^T分解求实对称矩阵特征值的递归算法

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

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Recursive algorithm for calculating eigenvalues of real symmetric matrix based on LDL^T decomposition

基于LDL^T分解求实对称矩阵特征值的递归算法