A Parallel Algorithm for the Multi-input Sylvester-Observer Equation

We present a new algorithm for solving the Multi-input Sylvester-Observer Equation. The algorithm embodies two main computational phases: the solution of a series of independent equation systems, and a series of matrix-matrix multiplications. As such, the algorithm is well suited for a parallel machine. By reducing the coefficient matrix to lower Hessenberg form, one can implement the algorithm efficiently, with few floating-point operations and little workspace. We present experimental results on the CRAY Y-MP and the Siemens S600/10 that confirm the efficiency of our algorithm.