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| 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. |
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| Keywords:signal and information processing; joint diagonalization; Jacobi-type; complex symmetric matrices; LU; LQ |
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