Relative gradient based algorithms for general joint diagonalization of complex matrices

This article deals with the problem of joint diagonalization of hermitian and/or complex symmetric matrices. Within the framework of gradient algorithms, we develop various algorithms which are based on different levels of approximation of the classical diagonalization criterion. The algorithms are based on a multiplicative update and on the derivation of an optimal step-size. One of the algorithms is a generalization of DOMUNG to the complex case. Finally, in the blind source separation context, computer simulations illustrate the relative performances of some proposed algorithms in comparison to the true gradient one.