Non-orthogonal joint diagonalization algorithm based on hybrid trust region method and its application to blind source separation

We proposed an algorithm for the efficient non-orthogonal joint diagonalization of a given set of matrices. The algorithm is based on the hybrid trust region method (HTRM) and its optimization approach, on which the efficiency of the method depends. Unlike traditional trust region methods that resolve sub-problems, HTRM efficiently searches a region via a quasi-Newton approach, by which it identifies new iteration points when a trial step is rejected. Thus, the proposed algorithm improves computational efficiency. Under mild conditions, we prove that the HTRM-based algorithm has global convergence properties together with local superlinear and quadratic convergence rates. Finally, we apply the combinative algorithm to blind source separation (BSS). Numerical results show that this method is highly robust, and computer simulations indicate that the algorithms excellently performs BSS.