# Software

## MESS

MESS (Matrix Equation Sparse Solver) is a MATLAB toolbox (i.e., a set of MATLAB routines) for the solution of certain large scale problems in control theory, which are closely related to Matrix equations (like Lyapunov or Riccati equations). It uses iterative algorithms and is intended for large, sparse problems.

Amongst other things, it can solve Lyapunov and Riccati equations, and perform model order reduction. Even though MESS has been implemented in MATLAB rather than programming languages like FORTRAN, C, this does not mean that MESS is restricted to the solution of "scientific toy problems". Several measures, such as the use of global variables for large data structures, have been taken to enhance the computational performance of MESS routines. To put this into the right perspective, Lyapunov equations of order larger than 20000 were solved by MESS within few mnutes on a regular laptop. When using standard methods, supercomputers are needed to solve problems of this size....more

## RRQR-MEX a MATLAB Mex-Interface for the rank revealing QR factorization

RRQR-MEX provides a MATLAB-MexInterface function to the FORTRAN RRQR implementation by G.Quintana-Orti and C.H. Bischof ...more

## Wachspress ADI-Shifts

An implementation of the elliptic integral based (sub)optimal alternating directions implicit (ADI) shift parameters following the theory by Wachspress et.al. ...more