When using standard (dense) methods, supercomputers are needed to solve problems of this size in reasonable time.įor citations to the Software please see the CITATION.md file in the top level directory of the corresponding download or installation. On a 64bit computeserver algebraic Riccati equations of order 250,000 can be solved in well below an hour and solutions to Lyapunov equations for 3d multiphysics applications with roughly 500,000 DOFs have been computed in only a few hours. within less than a minute on a regular laptop computer. To put this into the right perspective, Lyapunov equations of order 20,000 were solved by M.E.S.S. Several measures have been taken to enhance the computational performance of M.E.S.S. is therefore not restricted to the solution of "academic toy problems". has been implemented in MATLAB as well as C, with bindings also via MEX and to Python. can solve Lyapunov and Riccati equations, and perform model reduction of systems in state space and structured differential algebraic form. 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.Īmongst other things, M.E.S.S. The new version has been rewriten in large parts to fit the drastic upgrades in the Matlab releases since 2000. It is intended for solving large sparse matrix equations. is the successor to the LyaPack Toolbox for MATLAB.
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