中文摘要：

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。

英文摘要：

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.