diskutiert, basiert auf Schur-Zerlegung der Systemmatrix. In meiner alten Gruppe am MPI Magdeburg gibt es ein Softwarepaket (MESS), was u.a. auch diesen Löser implementiert hat, siehe
Vice versa, should we also try to use Matlab's builtin 'lyap' to solve Sylvester's equation? Probably NO, because we already know that for cases where one of the matrices is much smaller than the other, our 'sylv' code is (much!) faster than function 'lyap' contained in
Matlab's Control System Toolbox
Last edit: Burkhard Schmidt 2023-01-26
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Tobias Breiten (TU Berlin) writes me:
Die Version von Matlab ist im Wesentliche der Bartels-Stewart-Algorithmus, eine (modifzierte) Variante von diesem wurde im paper
DIRECT METHODS FOR MATRIX SYLVESTER AND LYAPUNOV EQUATIONS
by DANNY C. SORENSEN and YUNKAI ZHOU
diskutiert, basiert auf Schur-Zerlegung der Systemmatrix. In meiner alten Gruppe am MPI Magdeburg gibt es ein Softwarepaket (MESS), was u.a. auch diesen Löser implementiert hat, siehe
"lyap2solve.m" in https://csc.mpi-magdeburg.mpg.de/mpcsc/software/mess/mmess/2.2/MMESS-2.2.zip
Kann sicher nicht mit der Matlab-Implementierung mithalten, könnte ggf aber höhere Dimensionen zulassen.
Last edit: Burkhard Schmidt 2023-01-26
Vice versa, should we also try to use Matlab's builtin 'lyap' to solve Sylvester's equation? Probably NO, because we already know that for cases where one of the matrices is much smaller than the other, our 'sylv' code is (much!) faster than function 'lyap' contained in
Matlab's Control System Toolbox
Last edit: Burkhard Schmidt 2023-01-26
Availability of "Control System Toolbox" is checked in +prt/init.m using
But what about Octave?!?
Yes, Octave has an equivalent to Matlab's "Control System Toolbox"
Last edit: Burkhard Schmidt 2023-01-26
Lara Neureither sends me another Lyapunov solver based on the following publication:
Deterministic Continuation of Stochastic Metastable Equilibria via Lyapunov Equations and Ellipsoids
by Christian Kuehn
How good is it?