幂法求矩阵最大特征值.doc

幂法求矩阵最大特征值 摘要 在物理、力学和工程技术中的很多问题在数学上都归结为求矩阵特征值的问题，而在某些工程、物理问题中，通常只需要求出矩阵的最大的特征值（即主特征值）和相应的特征向量，对于解这种特征值问题，运用幂法则可以有效的解决这个问题。 幂法是一种计算实矩阵A的最大特征值的一种迭代法，它最大的优点是方法简单。对于稀疏矩阵较合适， 但有时收敛速度很慢。 用java来编写算法。这个程序主要分成了三个大部分：第一部分为将矩阵转化为线性方程组；第二部分为求特征向量的极大值；第三部分为求幂法函数块。其基本流程为幂法函数块通过调用将矩阵转化为线性方程组的方法，再经过一系列的验证和迭代得到结果。 关键词：幂法；矩阵最大特征值；java；迭代  POWER METHOD TO CALCULATE THE MAXIMUM EIGENVALUE MATRIX ABSTRACT In physics, mechanics and engineering technology of a lot of problems in math boil down to matrix eigenvalue problem, and in some engineering, physical problems, usually only the largest eigenvalue of the matrix (i.e., the main characteristics of the value) and the corresponding eigenvectors, the eigenvalue problem for solution, using the power law can effectively solve the problem. Power method is A kind of computing the largest eigenvalue of real matrix A of an iterative method, its biggest advantage is simple.For sparse matrix is right, but sometimes very slow convergence speed. Using Java to write algorithms.This program is mainly divided into three most: the first part for matrix can be converted to linear equations;The second part is the eigenvector of the maximum;The third part is the exponentiation method of function block.Its basic process as a power law function block by calling the method of matrix can be converted to linear equations, then after a series of validation and iteration to get the results. Key words: Power method; Matrix eigenvalue; Java; The iteration  目 录 1 幂