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In blind source separation problems it is assumed that the approximate diagonalization of a matrix set achieves more robust solutions than the simultaneous diagonalization of a matrix pencil. In this work we will analyse approximate diagonalization methods using a generalized eigendecomposition (GED) of any pair of a given matrix set. The constraints of GHD solutions provide a criterion to choose a matrix subset even when none of the matrices follows an ideal model. We also present some numerical simulations comparing the performance of the solutions achieved by the referred approaches.