A Numerical Algorithm for Block-Diagonal Decomposition of Matrix *-Algebras, Part I: Proposed Approach and Application to Semidefinite Programming

Motivated by recent interest in group-symmetry in semidefinite programming, we propose a numerical method for finding a finest simultaneous block-diagonalization of a finite number of matrices, or equivalently the irreducible decomposition of the generated matrix *-algebra. The method is composed of numerical-linear algebraic computations such as eigenvalue computation, and automatically makes full use of the … Read more