Geodesic
An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation
Electronic transactions on numerical analysis, Tome 33 (2009)
We present a new iterative method for the computation of approximate solutions to large-scale continuous-time algebraic Riccati equations. The proposed method is a projection method onto an extended block Krylov subspace, which can be seen as a sum of two block Krylov subspaces in A and A - 1. We give some theoretical results and present numerical experiments for large and sparse problems. These numerical tests show the efficiency of the proposed scheme as compared to the block Arnoldi and Newton-ADI methods.
Classification : 65F10, 65F30
Keywords: block arnoldi, extended block Krylov, low rank, Riccati equations 
@article{ETNA_2009__33__a8,
     author = {Heyouni,  M. and Jbilou,  K.},
     title = {An extended block {Arnoldi} algorithm for large-scale solutions of the continuous-time algebraic {Riccati} equation},
     journal = {Electronic transactions on numerical analysis},
     year = {2009},
     volume = {33},
     zbl = {1171.65035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2009__33__a8/}
}
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AU  - Jbilou,  K.
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%A Jbilou,  K.
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%J Electronic transactions on numerical analysis
%D 2009
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%F ETNA_2009__33__a8
Heyouni,  M.; Jbilou,  K. An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation. Electronic transactions on numerical analysis, Tome 33 (2009). http://geodesic.mathdoc.fr/item/ETNA_2009__33__a8/