Title :

Adaptive rational block Arnoldi methods for model reductions in large-scale MIMO dynamical systems

Author(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]
Abidi, Oussama [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]

Journal title :

New Trends in Mathematical Science

Pages :

227-239

Publication date :

2016-04-28

ISSN :

2147-5520

English keyword(s) :

Dynamical systems
model reduction
rational block Krylov subspaces
transfer functions

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

In recent years, a great interest has been shown towards Krylov subspace techniques applied to model order reduction of large-scale dynamical systems. A special interest has been devoted to single-input single-output (SISO) ...
Show more >In recent years, a great interest has been shown towards Krylov subspace techniques applied to model order reduction of large-scale dynamical systems. A special interest has been devoted to single-input single-output (SISO) systems by using moment matching techniques based on Arnoldi or Lanczos algorithms. In this paper, we consider multiple-input multiple-output (MIMO) dynamical systems and introduce the rational block Arnoldi process to design low order dynamical systems that are close in some sense to the original MIMO dynamical system. Rational Krylov subspace methods are based on the choice of suitable shifts that are selected a priori or adaptively. In this paper, we propose an adaptive selection of those shifts and show the efficiency of this approach in our numerical tests. We also give some new block Arnoldi-like relations that are used to propose an upper bound for the norm of the error on the transfer function.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL