We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and performance of the resulting methods with existing Sylvester solvers. The algorithms proposed here are easy to parallelize. We report on the parallelization of those algorithms and demonstrate their high efficiency and scalability using experimental results obtained on a cluster of Intel Pentium Xeon processors.

We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and performance of the resulting methods with existing Sylvester solvers. The algorithms proposed here are easy to parallelize. We report on the parallelization of those algorithms and demonstrate their high efficiency and scalability using experimental results obtained on a cluster of Intel Pentium Xeon processors.