A stable and efficient algorithm for difficult Non-Orthogonal Joint Diagonalization problems

This article deals with the Non-Orthogonal Joint Diagonalization of few matrices of large size: a difficult problem that is not solved by existing methods. The proposed algorithm combines, on the one hand, the efficiency provided by the Givens and hyperbolic rotations parametrization of the mixing matrix and, on the other hand, the stability guaranteed by the minimization of the complete off-diagonal norm. The stability and the quadratic convergence of the algorithm are illustrated by numerical simulations in situations where other techniques are slow or even non-convergent. The improvement is reached at the price of a moderate increase of the computational complexity.