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Numerical Algorithms
Erschienen in: Numerical Algorithms 4/2020

02.04.2020 | Original Paper

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

verfasst von: Fatemeh P. A. Beik, Khalide Jbilou, Mehdi Najafi-Kalyani, Lothar Reichel

Erschienen in: Numerical Algorithms | Ausgabe 4/2020

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Abstract

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.
Vorheriger Artikel RMVPIA: a new algorithm for computing the Lagrange multivariate polynomial interpolation
Nächster Artikel Identification of the source function for a seawater intrusion problem in unconfined aquifer

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Fußnoten
1
All computations for this section were carried out on a 64-bit 2.50-GHz core i5 processor with 8.00-GB RAM using MATLAB version 9.4 (R2018a).
 
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Metadaten
Titel
Golub–Kahan bidiagonalization for ill-conditioned tensor equations with applications
verfasst von
Fatemeh P. A. Beik
Khalide Jbilou
Mehdi Najafi-Kalyani
Lothar Reichel
Publikationsdatum
02.04.2020
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 4/2020
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00911-y

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