关键词: 矩阵, 非线性方程组, 最大特征值, 特征向量, 拟Newton法

Abstract: This paper is aimed to solve the maximum eigenvalue of high order matrix and its corresponding eigenvector through the method which transfers the equations into a higher order nonlinear equations. At the same time, this paper puts forward the Quasi-Newton method which can solve the maximum eigenvalue and its corresponding eigenvector, the rearranging formula and algorithm of Broyden methods are given to solve the maximum eigenvalue and the corresponding eigenvector; the rearranging formula and algorithm of BFS methods; the rearranging formula and algorithm of DFP methods. The judgment matrix of analytic hierarchy process is used as an example. The results show that the idea is feasible and the convergence speed is higher.

Key words: matrix, nonlinear equations, the maximum eigenvalue, eigenvector, Quasi-Newton methods