Improving accuracy of parallel SLICOT model reduction routines for stable systems

This paper shows part of the work carried out to develop parallel versions of the SLICOT routines for model reduction of stable systems. In particular, the routines that have been parallelised are those based on the solution of Lyapunov equations. The goal is to be able to work with larger unreduced models and also to obtain better performance in the reduction process. New routines have been developed using standard libraries to improve portability and efficiency. A preliminary version was released previously by the authors, which achieved high performance. However, accuracy improvements have been necessary in order to make the new routines similar to the sequential ones in this aspect. Routines presented in this paper preserve good performance obtained by the previous parallel implementation while maintaining high accuracy of sequential SLICOT routines.