A preconditioned block Arnoldi method for ...
Document type :
Compte-rendu et recension critique d'ouvrage
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Title :
A preconditioned block Arnoldi method for large Sylvester matrix equations
Author(s) :
Bouhamidi, A. [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Université du Littoral Côte d'Opale [ULCO]
Hached, M. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Heyouni, M. [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Université du Littoral Côte d'Opale [ULCO]
Jbilou, K. [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Université du Littoral Côte d'Opale [ULCO]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Université du Littoral Côte d'Opale [ULCO]
Hached, M. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Heyouni, M. [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Université du Littoral Côte d'Opale [ULCO]
Jbilou, K. [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Université du Littoral Côte d'Opale [ULCO]
Journal title :
Numerical Linear Algebra with Applications
Pages :
208-219
Publisher :
Wiley
Publication date :
2011-12-07
ISSN :
1070-5325
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
SUMMARY In this paper, we propose a block Arnoldi method for solving the continuous low‐rank Sylvester matrix equation AX + XB = EF T . We consider the case where both A and B are large and sparse real matrices, and E and ...
Show more >SUMMARY In this paper, we propose a block Arnoldi method for solving the continuous low‐rank Sylvester matrix equation AX + XB = EF T . We consider the case where both A and B are large and sparse real matrices, and E and F are real matrices with small rank. We first apply an alternating directional implicit preconditioner to our equation, turning it into a Stein matrix equation. We then apply a block Krylov method to the Stein equation to extract low‐rank approximate solutions. We give some theoretical results and report numerical experiments to show the efficiency of this method. Copyright © 2011 John Wiley & Sons, Ltd.Show less >
Show more >SUMMARY In this paper, we propose a block Arnoldi method for solving the continuous low‐rank Sylvester matrix equation AX + XB = EF T . We consider the case where both A and B are large and sparse real matrices, and E and F are real matrices with small rank. We first apply an alternating directional implicit preconditioner to our equation, turning it into a Stein matrix equation. We then apply a block Krylov method to the Stein equation to extract low‐rank approximate solutions. We give some theoretical results and report numerical experiments to show the efficiency of this method. Copyright © 2011 John Wiley & Sons, Ltd.Show less >
Language :
Anglais
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Non
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Submission date :
2024-01-16T05:08:59Z
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