Canonical Polyadic decomposition of complex-valued multi-way arrays based on Simultaneous Schur Decomposition

In this paper, we propose a new semi-algebraic algorithm to compute the Canonical Polyadic (CP) decomposition of complex-valued multi-way arrays. The proposed algorithm is based on the Simultaneous Schur Decomposition (SSD) of particular matrices derived from the array to process. This CP algorithm solves some convergence problems of classical iterative techniques and its identifiability assumptions are less restrictive than those of other semi-algebraic methods. We also propose a new Jacobi-like algorithm to calculate the SSD of several complex-valued matrices. Finally the usefulness of the proposed method is illustrated in the context of fluorescence spectroscopy and epileptic source localization.