Algorithm for Error-Controlled Simultaneous Block-Diagonalization of Matrices

An algorithm is given for the problem of finding the finest simultaneous block-diagonalization of a given set of square matrices. This problem has been studied independently in the area of semidefinite programming and independent component analysis. The proposed algorithm considers the commutant algebra of the matrix -algebra generated by the given matrices. It is simpler than other existing methods, and has the capability of controlling numerical errors. Some numerical examples are presented to demonstrate its merits.