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We present an improved version of the famous orthogonal joint diagonalization (JD) of a set of matrices, on the basis of successive Jacobi-like transformations. In particular, the Jacobi transformation matrix in each rotation step is only dependent on a single parameter that has analytical solution in real-value case. If this algorithm is improved, it can indirectly deal with the complex target matrices...
In this paper, two new algorithms are proposed for non-orthogonal joint matrix diagonalization under Hermitian congruence. The idea of these two algorithms is based on the so-called Jacobi algorithm for solving the eigenvalues problem of Hermitian matrix. The algorithms are then called ‘general Jabobi-like diagonalization’ algorithms (GERALD). They are based on the search of two complex parameters...
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