M-M.E.S.S, Matrix Equation Sparse Solvers (MESS): A MATLAB Toolbox for the Solution of Sparse Large-Scale Matrix Equations. MESS is the successor to the LyaPack Toolbox for MATLAB. It is intended for solving large sparse matrix equations. The new version has been rewriten in large parts to fit the drastic upgrades in the Matlab releases since 2000. Additionally new solvers for differential Riccati equations extend the functionality and many enhancements upgrade the efficiency and runtime behaviour enlarging the number of unknowns that can now be computed. Amongst other things, it can solve Lyapunov and Riccati equations, and do model reduction. Even though MESS has been implemented in MATLAB rather than programming languages like FORTRAN, C, or JAVA, this does not mean that MESS is restricted to the solution of”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 20000 were solved by MESS within few minutes on a regular laptop computer. On a 64bit computeserver algebraic Riccati equations of order 250 000 have been solved in less than 1 day. When using standard (dense) methods, supercomputers are needed to solve problems of this size.

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  1. Jin, Bo; Illingworth, Simon J.; Sandberg, Richard D.: Optimal sensor and actuator placement for feedback control of vortex shedding (2022)
  2. Liljegren-Sailer, Björn; Marheineke, Nicole: Input-tailored system-theoretic model order reduction for quadratic-bilinear systems (2022)
  3. Benner, Peter; Köhler, Martin; Saak, Jens: Matrix equations, sparse solvers: \textttM-M.E.S.S.-2.0.1 -- philosophy, features, and application for (parametric) model order reduction (2021)
  4. Benner, Peter; Werner, Steffen W. R.: Frequency- and time-limited balanced truncation for large-scale second-order systems (2021)
  5. Dorschky, Ines; Reis, Timo; Voigt, Matthias: Balanced truncation model reduction for symmetric second order systems -- a passivity-based approach (2021)
  6. Haasdonk, Bernard: MOR software (2021)
  7. Li, Dongping; Zhang, Xiuying; Liu, Renyun: Exponential integrators for large-scale stiff Riccati differential equations (2021)
  8. Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens: A numerical comparison of different solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems (2020)
  9. Benner, Peter; Werner, Steffen W. R.: Hankel-norm approximation of large-scale descriptor systems (2020)
  10. Kirsten, Gerhard; Simoncini, Valeria: Order reduction methods for solving large-scale differential matrix Riccati equations (2020)
  11. Zhang, Liping; Fan, Hung-Yuan; Chu, Eric King-wah: Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations (2020)
  12. Zhang, Liping; Fan, Hung-Yuan; Chu, Eric King-Wah: Krylov subspace methods for discrete-time algebraic Riccati equations (2020)
  13. Behr, Maximilian; Benner, Peter; Heiland, Jan: Solution formulas for differential Sylvester and Lyapunov equations (2019)
  14. Kürschner, Patrick: Approximate residual-minimizing shift parameters for the low-rank ADI iteration (2019)
  15. Pulch, Roland; Narayan, Akil: Balanced truncation for model order reduction of linear dynamical systems with quadratic outputs (2019)
  16. Yu, Bo; Fan, Hung-Yuan; Chu, Eric King-wah: Large-scale algebraic Riccati equations with high-rank constant terms (2019)
  17. Benner, Peter; Goyal, Pawan; Gugercin, Serkan: (\mathcalH_2)-quasi-optimal model order reduction for quadratic-bilinear control systems (2018)
  18. Benner, Peter; Qiu, Yue; Stoll, Martin: Low-rank eigenvector compression of posterior covariance matrices for linear Gaussian inverse problems (2018)
  19. Gosea, Ion Victor; Petreczky, Mihaly; Antoulas, Athanasios C.; Fiter, Christophe: Balanced truncation for linear switched systems (2018)
  20. Gosea, I. V.; Petreczky, M.; Antoulas, A. C.: Data-driven model order reduction of linear switched systems in the Loewner framework (2018)

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