Numerical solutions to large-scale ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Numerical solutions to large-scale differential Lyapunov matrix equations
Auteur(s) :
Hached, Mustapha [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Jbilou, Khalide [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
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.
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 >
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
Vulgarisation :
Non
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