On hybrid exact-approximate joint diagonalization

We consider a particular form of the classical approximate joint diagonalization problem, often encountered in maximum likelihood source separation based on second-order statistics with Gaussian sources. In this form the number of target-matrices equals their dimension, and the joint diagonality criterion requires that in each transformed (¿diagonalized¿) target-matrix, all off-diagonal elements on one specific row and column be exactly zeros, but does not care about the other (diagonal or off-diagonal) elements. We show that this problem always has a solution for symmetric, positive-definite target-matrices and present some interesting alternative formulations. We review two existing iterative approaches for obtaining the diagonalizing matrices and propose a third one with faster convergence.