New Simultaneous Generalized Schur Decomposition methods for the computation of the Canonical Polyadic decomposition

In signal processing several problems have been formulated as Simultaneous Generalized Schur Decomposition (SGSD) problems. Applications are found in blind source separation and multidimensional harmonic retrieval. Furthermore, SGSD methods for computing a third-order Canonical Polyadic (CP) decomposition have been proposed. The original SGSD method requires that all three matrix factors of the CP decomposition have full column rank. We first propose a new version of the SGSD method for computing a third-order CP decomposition. The proposed method mainly differs from the existing method in the way the triangular matrices are computed. Second, we propose an alternative SGSD method which only requires that two of the matrix factors of the CP decomposition have full column rank.