Numerical solutions to large-scale differential Lyapunov matrix equations

Hached, Mustapha; Jbilou, Khalide

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1007/s11075-017-0458-y

Permalink :

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

Title :

Numerical solutions to large-scale differential Lyapunov matrix equations

Author(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]

Journal title :

Numerical Algorithms

Pages :

741-757

Publisher :

Springer Verlag

Publication date :

2018-11

ISSN :

1017-1398

English keyword(s) :

Extended block Krylov
Low rank
Differential Lyapunov equations

HAL domain(s) :

Mathématiques [math]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T14:21:50Z

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