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

M. Heyouni and K. Jbilou

### Abstract

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]

### Key words

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

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