Generalized fractional algebraic linear system solvers - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Scientific Computing Année : 2022

Generalized fractional algebraic linear system solvers

Résumé

This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that is finding x solution to $∑α∈R$A$αx$=$b$. These systems will be referred to as Generalized Fractional Algebraic Linear Systems (GFALS). In this paper, we derive several gradient methods for solving these very computationally complex problems, which themselves require the solution to intermiediate standard Fractional Algebraic Linear Systems (FALS) $Aαx$=$b$, with $α∈R+$. The latter usually require the solution to many classical linear systems $Ax$=$b$. We also show that in some cases, the solution to a GFALS problem can be obtained as the solution to a first-order hyperbolic system of conservation laws. We also discuss the connections between this PDE-approach and gradient-type methods. The convergence analysis is addressed and some numerical experiments are proposed to illustrate and compare the methods which are proposed in this paper.
Fichier principal
Vignette du fichier
paperHAL.pdf (1.46 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03085997 , version 1 (22-12-2020)

Identifiants

Citer

Xavier Antoine, Emmanuel Lorin. Generalized fractional algebraic linear system solvers. Journal of Scientific Computing, 2022, 91, pp.25. ⟨10.1007/s10915-022-01785-z⟩. ⟨hal-03085997⟩
89 Consultations
92 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More