Fast Jacobi like algorithms for joint diagonalization of complex symmetric matrices

In this paper, we consider the problem of non-orthogonal joint diagonalization of a set of complex symmetric matrices. This appears in many signal processing problems, especially in source separation. We propose three new algorithms based on LU decomposition of the matrix we are looking for and based on a Jacobi like procedure. The algorithms are based on a coupled and a decoupled parameter estimation. Numerical simulations are provided to compare the performances with a similar one existing in the real case and adapted to the complex symmetric case. Finally, we propose a mixed algorithm combining two proposed ones which allows more balanced performances.