求矩阵特征值及特征向量的一种梯度逼近法

A Gradient Approximating Method of Finding Eigenvalues and Eigenvectors ofa Matrix

本文对于正定对称矩阵构造了一种新的向量迭代算法,它具有幂法在计算上简单、公式单一的优点,并且可以求出全部的特征值与特征向量。这种方法具有明确的几何背景。

The power method is a commonly used vector iterative method of finding eigenvalue of a matrix. However, this method can only find out the dominant eigenvalue and the corresponding eigenvector. In this paper for positive definite matrices粀e construct another new vector iterative algorithm, which is as simple and straightforward in computation as power method,moreover it can find out all of the eigenvalues and eigenvectors. This method has clear and definite geometric background.