求特征值的Jacobi方法

摘要

讨论了求实对称矩阵的特征值的经典Jacobi方法，通过一系列的正交相似变换将实对称矩阵化为对角矩阵，从而求出全部特征值和相应的特征向量。文中给出所有正交变换的计算公式，并用MATLAB编程实现，为实际问题的计算提供了简单实用的计算工具。%This paper addresses classical Jacobi method of eigenvalues calculation of a real symmetric matrix. It converts a real symmetric matrix into a diagonal matrix by a series of orthogonal similarity transformations, and then derives all eigenvalues and their corresponding eigenvectors. The paper presents the formulas of all orthogonal transformations, which are implemented by MATLAB programming. This provides a simple and practical calculation tool for the computation of practical problems.