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Journal Articles Numerical Algorithms Year : 2020

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

Fatemeh Beik
  • Function : Author
Mehdi Najafi-Kalyani
  • Function : Author
Lothar Reichel
  • Function : Author

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

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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⟩
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