矩阵的特征值计算方法探讨  

The Calculation Method of the Eigenvalues of the Matrix

作　　者：郏卫士 

机构地区：[1]湖北大学数学与统计学学院,武汉430000

出　　处：《德州学院学报》2017年第2期1-8,共8页Journal of Dezhou University

摘　　要：矩阵的特征值是矩阵应用的一个重点,在科学研究方面具有重要的地位,进行矩阵特征值的讨论可以直接用来解决实际的问题.本文简要介绍了矩阵特征值的普通求法,并着重研究求解矩阵的一些其他优化方法,包括幂法、反幂法、Jacobi方法、QR方法.在实际求解矩阵特征值问题时,根据矩阵的不同特点,选择最快速的方法求解,从而可以达到最优化解决实际问题.The eigenvalue of the matrix is one of the keys of the application of matrix, which has an impor- tant position in scientific research, matrix eigenvalue discussions can be directly used to solve practical problem. This paper briefly introduces the common matrix eigenvalue calculation methods, and focuses on a few other optimization methods for solving matrix. Some of the other optimization methods including power method, inverse power method, Jacobi method and QR method. However, in actual solving matrix eigenvalue problem, according to the different characteristics of the matrix, choose the fastest way to solve, in order to achieve optimization to solve practical problems.

关 键 词：矩阵特征值 幂法 反幂法 JACOBI方法 QR方法 

分 类 号：O151.21[理学—数学]