Title :

On an Economic Arnoldi Method for BML Matrices

Author(s) :

Beckermann, Bernhard [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Mertens, Clara [Auteur]
Department of Computer Science - K.U.Leuven
Vandebril, Raf [Auteur]
Department of Computer Science - K.U.Leuven

Journal title :

SIAM Journal on Matrix Analysis and Applications

Pages :

737-768

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2018-01

ISSN :

0895-4798

English keyword(s) :

Krylov subspace methods
Arnoldi method
semiseparable matrices

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Analyse classique [math.CA]

English abstract : [en]

Matrices whose adjoint is a low rank perturbation of a rational function of the matrix naturally arise when trying to extend the well known Faber-Manteuffel theorem, which provides necessary and sufficient conditions for ...
Show more >Matrices whose adjoint is a low rank perturbation of a rational function of the matrix naturally arise when trying to extend the well known Faber-Manteuffel theorem, which provides necessary and sufficient conditions for the existence of a short Arnoldi recurrence. We show that an orthonormal Krylov basis for this class of matrices can be generated by a short recurrence relation based on GMRES residual vectors. These residual vectors are computed by means of an updating formula. Furthermore, the underlying Hessenberg matrix has an accompanying low rank structure, which we will investigate closely.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T17:51:55Z