摘要
本文提出了两种针对复对称矩阵的雅可比联合对角化算法。目前虽然已经存在很多解决复值联合对角化问题的算法,但对于复值对称矩阵的研究较少,这种矩阵结构会出现在非圆复信号的伪协方差矩阵及张量分解问题中。本文算法的思想是利用基于LU或LQ分解的雅克比旋转矩阵,将要求解的对角化矩阵近似表示为一系列只有一个或两个参数的基本三角矩阵或酉矩阵,这样高维最小化问题就可以迭代地转化为一系列低维子问题。数值仿真验证了所提算法的性能,并与其它算法进行了比较。
In this paper, we propose two joint diagonalization algorithms of Jacobi-type for a set of complex and symmetric matrices. Many existing algorithms aim at the complex-valued JD problem, but few works have been done for symmetric one, which emerges in the pseudo-covariance matrix of improper complex signals or sometimes in tensor decomposition problem. The proposed methods resort to Jacobi rotation matrices based on LU or LQ decompositions. The diagonalizer matrix could be appropriately parameterized by a sequence of simple elementary triangular or unitary matrices, which depend on only one or two parameters. As such, the high-dimensional minimization problems could be replaced by a sequence of simple lower-dimensional ones in an iterative manner. Compared with another method, numerical simulations demonstrate the performance of the proposed methods.
出处
《新型工业化》
2013年第3期77-84,共8页
The Journal of New Industrialization
基金
supported in part by Fundamental Research Fund for Central Universities of China
Doctoral Fund of Ministry of Education of China under grant 20110041120019
National Natural Science Foundation of China under grants 60971097,61072098,and 61105008
关键词
信号与信息处理
联合对角化
雅可比
复对称矩阵
LU
LQ
signal and information processing
joint diagonalization
Jacobi-type
complex symmetric matrices
LU
LQ
