一种求解复Hermite矩阵特征值的方法

High Quality Method for Solving Eigenvalues of Complex Hermite Matrix

介绍几种求解矩阵特征值和特征向量的经典算法及各自优缺点,通过理论推导,提出了一种性能稳健的方法,可以求解信号处理中常见的复H erm ite阵。将对复H erm ite矩阵求特征值和特征向量的问题转化为求解实对称阵的特征值和特征向量,而实对称阵的求解采用一种改进的三对角Househo lder法。最后把结果与M atlab仿真结果比较,可以看出该方法有很高的精确度。

Several kinds of classic algorithms for solving eigenvalues and eigenvectors of the matrix are presented. Then by the theoretical deduction, a reliable method is used to solve a complex Hermite matrix in signal proceeding. The problems of eigenvalues and eigenvectors of the complex Hermite matrix can be tranformed to evaluate a real symmetric ones of the matrix. The improved Householder method is used to calculate the real symmetric matrix. Finally, compared with the Matlab result, the method has a high precision.