拟Newton法在高阶矩阵中的应用——求解最大特征值及特征向量  

Quasi-Newton methods for solving maximum eigenvalue and its corresponding eigenvector of high order matrix

作　　者：何超[1] 刘西林[1] 李佳珍[1] 

机构地区：[1]西北工业大学管理学院,西安710129

出　　处：《计算机工程与应用》2012年第16期33-36,84,共5页Computer Engineering and Applications

摘　　要：将求解高阶矩阵的最大特征值及其对应的特征向量问题转化为高阶非线性方程组的求解问题。在此基础上,提出了求解矩阵最大特征值及其对应特征向量的拟Newton法,给出求解矩阵最大特征值及其单位化向量重新整理后的Broyden方法公式、BFS方法公式、DFP方法公式及其对应的Broyden算法,BFS算法,DFP算法。以层次分析法中高阶判断矩阵为例验证了该方法的可行性,说明了该方法相对收敛速度快的优势。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.

关 键 词：矩阵 非线性方程组 最大特征值 特征向量 拟NEWTON法 

分 类 号：O24[理学—计算数学]