Geodesic
Low-rank iterative methods for projected generalized Lyapunov equations
Electronic transactions on numerical analysis, Tome 30 (2008), pp. 187-202
We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximations to the solution of projected generalized Lyapunov equations with low-rank symmetric, positive semidefinite right-hand side. Numerical examples are presented.
Classification : 65F10, 65F30, 15A22, 15A24
Keywords: projected generalized Lyapunov equations, alternating direction implicit method, smith method, low-rank approximation 
@article{ETNA_2008__30__a14,
     author = {Stykel,  Tatjana},
     title = {Low-rank iterative methods for projected generalized {Lyapunov} equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {187--202},
     year = {2008},
     volume = {30},
     zbl = {1171.65385},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__30__a14/}
}
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%A Stykel,  Tatjana
%T Low-rank iterative methods for projected generalized Lyapunov equations
%J Electronic transactions on numerical analysis
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Stykel,  Tatjana. Low-rank iterative methods for projected generalized Lyapunov equations. Electronic transactions on numerical analysis, Tome 30 (2008), pp. 187-202. http://geodesic.mathdoc.fr/item/ETNA_2008__30__a14/