NUMERICAL SOLUTION OF DISCRETE STABLE LINEAR MATRIX EQUATIONS ON MULTICOMPUTERS

Abstract

We investigate the parallel performance of numerical algorithms for solving discrete Sylvester and Stein equations as they appear for instance in discrete-time control problems, filtering, and image restoration. The methods used here are the squared Smith iteration and the sign function method on a Cayley transformation of the original equation. For Stein equations with semidefinite right-hand side these methods are modified such that the Cholesky factor of the solution can be computed directly without forming the solution matrix explicitly. We report experimental results of these algorithms on distributed-memory multicomputers