Low-rank approximate solutions to large-scale differential matrix Riccati equations

Guldoğan, Y.; Hached, Mustapha; Jbilou, Khalide; Kurulay, M.

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.4064/am2355-1-2018

Title :

Low-rank approximate solutions to large-scale differential matrix Riccati equations

Author(s) :

Guldoğan, Y. [Auteur]
Yildiz Technical University [YTU]
Hached, Mustapha [Auteur]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Jbilou, Khalide [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Kurulay, M. [Auteur]
Yildiz Technical University [YTU]

Journal title :

Applicationes Mathematicae

Pages :

233-254

Publisher :

Polish Academy of Sciences

Publication date :

2018

ISSN :

1233-7234

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We consider large-scale continuous-time differential matrix Riccati equations. The two main approaches proposed in the literature are based on a splitting scheme or on Rosenbrock / Backward Differentiation Formula (BDF) ...
Show more >We consider large-scale continuous-time differential matrix Riccati equations. The two main approaches proposed in the literature are based on a splitting scheme or on Rosenbrock / Backward Differentiation Formula (BDF) methods. The approach we propose is based on the reduction of the problem dimension prior to integration. We project the initial problem onto an extended block Krylov subspace and obtain a low-dimensional differential matrix Riccati equation. The latter matrix differential problem is then solved by the BDF method and the solution obtained is used to reconstruct an approximate solution of the original problem. This process is repeated with increasing dimension of the projection subspace until achieving a chosen accuracy. We give some theoretical results and a simple expression of the residual allowing the implementation of a stop test in order to limit the dimension of the projection space. Some numerical experiments are reported.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

1612.00499
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