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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, two Jacobian joint diagonalization algorithms for complex symmetric matrices are proposed. Although there are many algorithms to solve complex co-diagonalization problems, there are few researches on complex-valued symmetric matrices, which appear in the pseudo-covariance matrix and tensor decomposition of non-circular complex signals. The idea of this algorithm is to use the Jacobi rotation matrix based on LU or LQ decomposition to approximate the diagonalized matrix to be solved as a series of basic triangular or unitary matrices with only one or two parameters so that the problem of high dimensional minimization It can be iteratively transformed into a series of low-dimensional sub-problems. Numerical simulation verifies the performance of the proposed algorithm and compares it with other algorithms.