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In the present paper, we are interested in developing iterative Krylovsubspace methods in tensor structure to solve a class of multilinear systemsvia Einstein product. In particular, we develop global variants of the GMRESand Gloub--Kahan bidiagonalization processes in tensor framework. We furtherconsider the case that mentioned equation may be possibly corresponds to adiscrete ill-posed problem. Applications arising from color image and videorestoration are included.

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