MESS swMATH ID: 14886 Software Authors: Saak, J., Mena, H., Benner, P. Description: 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. Homepage: http://www2.mpi-magdeburg.mpg.de/mpcsc/software/mess.php?lang=en Dependencies: Matlab Related Software: Matlab; RADI; MORLAB; LYAPACK; Loewner; Algorithm 432; sssMOR; benchmodred; mftoolbox; GRANSO; Chebfun; FEniCS; MORPACK; Morembs; pyMOR; RICPAC; SparseMatrix; SLICOT; redbKIT; MATLAB expm Cited in: 32 Publications all top 5 Cited by 60 Authors 8 Benner, Peter 7 King-wah Chu, Eric 4 Fan, Hung-Yuan 4 Weng, Peter Chang-Yi 3 Saak, Jens 3 Werner, Steffen W. R. 2 Antoulas, Athanasios C. 2 Gosea, Ion Victor 2 Heiland, Jan 2 Kürschner, Patrick 2 Li, Tiexiang 2 Lin, Wen-Wei 2 Petreczky, Mihály 2 Zhang, Liping 1 Ahmad, Mian Ilyas 1 Baars, Sven 1 Behr, Maximilian 1 Bini, Dario Andrea 1 Bujanović, Zvonimir 1 Dijkstra, Henk A. 1 Dorschky, Ines 1 Du, Xin 1 Fiter, Christophe 1 Goyal, Pawan 1 Gugercin, Serkan 1 Haasdonk, Bernard 1 Hamadi, M. A. 1 Hund, Manuela 1 Iannazzo, Bruno 1 Illingworth, Simon J. 1 Jbilou, Khalide 1 Jin, Bo 1 Kirsten, Gerhard 1 Köhler, Martin 1 Kühn, Christian 1 Li, Dongping 1 Liljegren-Sailer, Björn 1 Liu, Renyun 1 Mak, Simon 1 Marheineke, Nicole 1 Meini, Beatrice 1 Mitchell, Tim 1 Mlinarić, Petar 1 Mulder, Thomas E. 1 Narayan, Akil C. 1 Pulch, Roland 1 Qiu, Yue 1 Ratnani, Ahmed 1 Reis, Timo 1 Sandberg, Richard D. 1 Simoncini, Valeria 1 Sreeram, Victor 1 Stillfjord, Tony 1 Stoll, Martin 1 Viebahn, J. P. 1 Voigt, Matthias 1 Wubs, Fred W. 1 Zhang, Ruda 1 Zhang, Xiuying 1 Zulfiqar, Umair all top 5 Cited in 15 Serials 6 SIAM Journal on Scientific Computing 5 Journal of Computational and Applied Mathematics 3 SIAM Journal on Matrix Analysis and Applications 3 Numerical Algorithms 2 Applied Numerical Mathematics 2 Advances in Computational Mathematics 1 Journal of Computational Physics 1 Journal of Fluid Mechanics 1 Calcolo 1 Linear Algebra and its Applications 1 Computational Optimization and Applications 1 ETNA. Electronic Transactions on Numerical Analysis 1 SIAM/ASA Journal on Uncertainty Quantification 1 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Fundamentals of Algorithms all top 5 Cited in 14 Fields 20 Systems theory; control (93-XX) 19 Numerical analysis (65-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 5 Partial differential equations (35-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Fluid mechanics (76-XX) 2 Statistics (62-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Geophysics (86-XX) Citations by Year