**In minisymposium: Eigenvalue Computations and Applications**

Joint block diagonalization (JBD/JBD) problem is to find a congruence transformation matrix such that several given matrices under such transformation are all exactly or approximately block diagonal matrices with the same prescribed nonzero pattern. General JBD (GJBD) problem is to find a block diagonal structure with the maximum number of diagonal blocks such that there exist solutions to the corresponding JBD/JBD problem. JBD/GJBD problem can be deemed as a decomposition of a third order tensor, it arises in blind source separation with many important applications. In this talk, I will show that GJBD problem is strongly connected with a structured matrix polynomial, whoes coefficint matrices are the given matrices. The solutions to the GJBD problem are characterized via the eigeninformation of the matrix polynomial. Numerical method is proposed to solve the GJBD problem.