Differential equations and solution of ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Differential equations and solution of linear systems
Author(s) :
Laminie, Jacques [Auteur]
Laboratoire de Mathématiques Informatique et Applications [LAMIA]
Chehab, Jean-Paul [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Laboratoire de Mathématiques Informatique et Applications [LAMIA]
Chehab, Jean-Paul [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Journal title :
Numerical Algorithms
Pages :
103-124
Publisher :
Springer Verlag
Publication date :
2005
ISSN :
1017-1398
English keyword(s) :
Differential equation
Numerical schemes
Numerical linear algebra
Preconditioning
Numerical schemes
Numerical linear algebra
Preconditioning
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [en]
Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretisation of differential systems. In this article the authors propose generating numerical ...
Show more >Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretisation of differential systems. In this article the authors propose generating numerical methods in numerical linear algebra by modelling the linear system to be solved as a given state of a dynamical system; the solution can be reached asymptotically, as a (asymptotically stable) steady state, but also as a finite time (shooting methods). In that way, any (stable) numerical scheme for the integration of such a problem can be presented as a method for solving linear systems. The authors discuss aspects of this approach, which allows them to recover some known methods but also to introduce new ones. Finally, some convergence results and numerical illustrations are presented.Show less >
Show more >Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretisation of differential systems. In this article the authors propose generating numerical methods in numerical linear algebra by modelling the linear system to be solved as a given state of a dynamical system; the solution can be reached asymptotically, as a (asymptotically stable) steady state, but also as a finite time (shooting methods). In that way, any (stable) numerical scheme for the integration of such a problem can be presented as a method for solving linear systems. The authors discuss aspects of this approach, which allows them to recover some known methods but also to introduce new ones. Finally, some convergence results and numerical illustrations are presented.Show less >
Language :
Anglais
Popular science :
Non
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