Experimental evaluation of new SLICOT solvers for linear matrix equations based on the matrix sign function

We describe new solvers for linear matrix equations implemented in the Subroutine Library in Control Theory (SLICOT). These solvers are based on the matrix sign function method and can be applied to stable Lyapunov and Sylvester equations which frequently arise in analysis and synthesis of control systems and in particular in model reduction. The implemented algorithms are specially suited for large problems with dense, unstructured matrices and are enhanced by new scaling strategies. The numerical results illustrate the advantages of using the new SLICOT solvers.