A Parallel Algorithm for the Sylvester Observer Equation

We present a new algorithm for solving the Sylvester-Observer Equation: AX ? XH = (0;C). The algorithm embodies two main computational phases: the solution of a series of independent equation systems, and a series of matrix-matrix multiplications. The algorithm is, thus, well suited for parallel and high performance computing. By reducingthe coeecient matrix A to lower Hessenberg form, one can implementthe algorithmeeciently, with few oating-point operations and little workspace. The algorithm has been succesfully implemented on a Cray C-90. A comparison, both theoretical and experimental, has been made with the well-known Hessenberg-Schur algorithm which solves an arbitrary Sylvester equation. Our theoretical analysis and experimental results connrm the superiority of the proposed algorithm, both in eeciency and speed, over the Hessenberg-Schur algorithm.