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