Numerical solutions to large-scale differential Lyapunov matrix equations

Hached, Mustapha; Jbilou, Khalide

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1007/s11075-017-0458-y

URL permanente :

http://hdl.handle.net/20.500.12210/121688

Titre :

Numerical solutions to large-scale differential Lyapunov matrix equations

Auteur(s) :

Hached, Mustapha [Auteur correspondant]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Jbilou, Khalide [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]

Titre de la revue :

Numerical Algorithms

Pagination :

741-757

Éditeur :

Springer Verlag

Date de publication :

2018-11

ISSN :

1017-1398

Mot(s)-clé(s) en anglais :

Extended block Krylov
Low rank
Differential Lyapunov equations

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The ...
Lire la suite >In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The first approach is based on the integral expression of the exact solution and an approximation method for the computation of the exponential of a matrix times a block of vectors. In the second approach, we first project the initial problem onto a block (or extended block) Krylov subspace and get a low-dimensional differential Lyapunov matrix equation. The latter differential matrix problem is then solved by the Backward Differentiation Formula method (BDF) and the obtained solution is used to build a low rank approximate solution of the original problem. The process is being repeated, increasing the dimension of the projection space until some prescribed accuracy is achieved. We give some new theoretical results and present numerical experiments.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T14:21:50Z

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