Golub–Kahan bidiagonalization for ill-conditioned tensor equations with applications - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Numerical Algorithms Année : 2020

Golub–Kahan bidiagonalization for ill-conditioned tensor equations with applications

Fatemeh Beik
  • Fonction : Auteur
Mehdi Najafi-Kalyani
  • Fonction : Auteur
Lothar Reichel
  • Fonction : Auteur

Résumé

This paper is concerned with the solution of severely ill-conditioned linear tensor equations. These kinds of equations may arise when discretizing partial differential equations in many space-dimensions by finite difference or spectral methods. The deblurring of color images is another application. We describe the tensor Golub–Kahan bidiagonalization (GKB) algorithm and apply it in conjunction with Tikhonov regularization. The conditioning of the Stein tensor equation is examined. These results suggest how the tensor GKB process can be used to solve general linear tensor equations. Computed examples illustrate the feasibility of the proposed algorithm.
Fichier non déposé

Dates et versions

hal-04413529 , version 1 (23-01-2024)

Identifiants

Citer

Fatemeh Beik, Khalide Jbilou, Mehdi Najafi-Kalyani, Lothar Reichel. Golub–Kahan bidiagonalization for ill-conditioned tensor equations with applications. Numerical Algorithms, 2020, International Conference Mathematical Modelling with Applications (Mohammed V University, Rabat Morocco, 1-4, April 2019), 84 (4), pp.1535-1563. ⟨10.1007/s11075-020-00911-y⟩. ⟨hal-04413529⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More