MESS, the Matrix Equations and Sparse Solvers library, is the successor to the Lyapack Toolbox for MATLAB. It is available as a MATLAB toolbox, as well as, a C-library. It is intended for solving large sparse matrix equations as well as problems from model order reduction and optimal control. The C version provides a large set of auxiliary subroutines for sparse matrix computations and efficient usage of modern multicore workstations.
Features
A list of the main features (some partially finished at the current stage) of both the MATLAB and C versions is:
- Solvers for large and sparse matrix Riccati (algebraic and differential) and Lyapunov (algebraic) equations
- Balanced Truncation based MOR for first and second order state space systems and index 1 DAEs
-MOR via the IRKA and TSIA algorithms- Basic tools for Large sparse linear quadratic optimal control problems
The C version moreover provides:
- sophisticated Multicore parallelism
- compressed file I/O
- uniform access to linear algebra routines
- specially structured Sylvester equation solvers
- interfaces to BLAS, LAPACK, Suitesparse, Slicot
Further Reading
- P. Benner, M. Köhler, J. Saak; Matrix equations, sparse solvers: M-M.E.S.S.-2.0.1 - philosophy, features and application for (parametric) model order reduction; In: Model Reduction of Complex Dynamical Systems, pp. 369 - 392 (Eds. Benner, P.; Breiten, T.; Faßbender, H.; Hinze, M.; Stykel, T. et al.). Birkhäuser, Cham, Switzerland, 2021 DOI BibTeX.
- J. Saak, M. Voigt; Model reduction of constrained mechanical systems in M-M.E.S.S; IFAC-PapersOnLine, 51(2): 661–666, 2018. DOI BibTeX
- P. Benner, J. Saak; Efficient solution of large scale Lyapunov and Riccati equations arising in model order reduction problems; Proceedings in Applied Mathematics and Mechanics, 8(1), Wiley InterScience; 2008. DOI.