Algorithms for joint block diagonalization

We present, in this paper, several algorithms for the joint block diagonalization (JBD) of a set of matrices. In particular, we will show and explain how the JBD can be achieved (up to a permutation matrix) using a Jacobi-like joint diagonalization algorithm. Two simple techniques are proposed to reduce the permutation indeterminacy to a `block permutation' indeterminacy (the latter being inherent to the JBD problem). Finally, a comparative study of the considered JBD methods is provided.