Matrix joint block diagonalization problem is a particular block term
decomposition of third order tensors, which  has many
important applications in blind source separation and independent
component analysis. In this talk, I will talk about two classes
of algebraic methods for JBD problem: one is based on matrix
polynomial, the other is based on matrix commutation.
Existence and uniqueness conditions for JBD problem are discussed.
Numerical methods are developed and validated by simulating examples.