On a Distributed Design and Implementation for a Matrix Equation

We present an eecient design and implementation for the solution of the Sylvester Observer matrix equation on a distributed memory computer. It consists of two main computational intensive segments, and one of a lesser complexity: the reduction of the system matrix A to a Hessenberg form, the solution of n shifted Hessenberg systems and a number of matrix-matrix multiplies. The Hessenberg reduction is solved eeciently by using appropriate routines from the ScaLAPACK package while the system solves are designed using a pipelined scheme on distributed memory computers and improved data reuse. We provide timings of our implementation on the Intel Paragon (TM) Supercomputer which demonstrates both speed and eeciency of the proposed algorithm.