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

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....

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Bibliographic Details
Published in:Numerical algorithms 2020-08, Vol.84 (4), p.1535-1563
Main Authors: Beik, Fatemeh P. A., Jbilou, Khalide, Najafi-Kalyani, Mehdi, Reichel, Lothar
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Color imagery
Computer Science
Conditioning
Eigenvalues
Iterative methods
Mathematical analysis
Mathematics
Numeric Computing
Numerical Analysis
Original Paper
Partial differential equations
Regularization
Spectral methods
Tensors
Theory of Computation
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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00911-y