RECSY – A High Performance Library for Sylvester-Type Matrix Equations

Abstract

RECSY is a library for solving triangular Sylvester-type matrix equations. Its objectives are both speed and reliability. In order to achieve these goals, RECSY is based on novel recursive blocked algorithms, which call high-performance kernels for solving small-sized leaf problems of the recursion tree. In contrast to explicit standard blocking techniques, our recursive approach leads to an automatic variable blocking that has the potential of matching the memory hierarchies of today’s HPC systems. The RECSY library comprises a set of Fortran 90 routines, which uses recursion and OpenMP for shared memory parallelism to solve eight different matrix equations, including continuous-time as well as discrete-time standard and generalized Sylvester and Lyapunov equations. Uniprocessor and SMP parallel performance results of our recursive blocked algorithms and corresponding routines in state-of-the-art libraries LAPACK and SLICOT are presented. The performance improvements of our recursive algorithms are remarkable, including 10-fold speedups compared to standard algorithms.