Volume 33, pp. 53-62, 2008-2009.

An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation

M. Heyouni and K. Jbilou


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.

Full Text (PDF) [134 KB], BibTeX

Key words

Block Arnoldi; Extended block Krylov; Low rank; Riccati equations.

AMS subject classifications

65F10, 65F30

Links to the cited ETNA articles

[8]Vol. 29 (2007-2008), pp. 136-149 Peter Benner, Hermann Mena, and Jens Saak: On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations

ETNA articles which cite this article

Vol. 43 (2014-2015), pp. 45-59 Said Agoujil, Abdeslem H. Bentbib, Khalide Jbilou, and El Mostafa Sadek: A minimal residual norm method for large-scale Sylvester matrix equations
Vol. 54 (2021), pp. 68-88 Peter Benner and Davide Palitta: On the solution of the nonsymmetric T-Riccati equation

< Back