基于QR分解的方阵特征多项式数值算法

摘要

Drawing on the concept of QR decomposition,we discuss the numerical algorithm of solving square matrix characteristicpolynomial in the way of using QR decomposition.This provides the condition for solving the characteristic polynomial of the matrix by Matlabprogramming.We verify that the numerical method can solve the characteristic polynomial of general square matrix well by computing theexamples of three square matrixes with different types,it is relatively simpler than the common method of solving the determinant withvariables and the trace-based algorithm,in particular,it has more apparent advantage for high-order square matrix,and is easy to implementon computer with Matlab programming,therefore this explains that the algorithm has higher applied value.%借鉴QR分解的概念，探讨如何利用QR分解法求一个方阵的特征多项式的数值算法。这就为用Matlab编程求解矩阵的特征多项式提供了条件。通过对三个不同类型矩阵的实例计算验证了该数值方法能够较好地求解一般方阵的特征多项式，比用通常的求带变量的行列式的方法和基于迹的算法要相对简单些，特别是对于高阶矩阵，其优势更加明显，且易在计算机上用Matlab编程实现，从而说明了该算法具有较高的实用价值。