Efficient algorithms for the block Hessenberg form

We investigate in this paper the performance of parallel algorithms for com puting the controllable part of a control linear system, with application t o the computation of minimal realizations. Our approach is based on a metho d that transforms the matrices of the system to block Hessenberg form by us ing rank-revealing orthogonal factorizations. The experimental analysis on a high performance architecture includes two r ank-revealing numerical tools: the SVD and the rank-revealing QR factorizat ions. Results are also reported, using the rank-revealing QR factorizations , on a parallel distributed architecture.