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Tensor GMRES and Golub-Kahan Bidiagonalization methods via the Einstein product with applications to image and video processing

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arxiv 2005.07458 v1 pith:5QTJPPKE submitted 2020-05-15 math.NA cs.NA

M. El Guide , A. El Ichi , F.P.A Beik , K. Jbilou This is my paper · ORCID
classification math.NAcs.NA
keywords tensorapplicationsbidiagonalizationeinsteingmresimagemethodsproduct
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In the present paper, we are interested in developing iterative Krylov subspace methods in tensor structure to solve a class of multilinear systems via Einstein product. In particular, we develop global variants of the GMRES and Gloub--Kahan bidiagonalization processes in tensor framework. We further consider the case that mentioned equation may be possibly corresponds to a discrete ill-posed problem. Applications arising from color image and video restoration are included.

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  1. Efficient iterative techniques for solving tensor problems with the T-product

    math.NA 2025-04 conditional novelty 4.0 of 10

    Conjugate-gradient-type iterative methods are formulated directly for T-product tensor equations, with finite-termination proofs and numerical demonstrations.

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