Some iterative approaches for Sylvester tensor equations, Part I: A tensor format of truncated Loose Simpler GMRES

Saberi-Movahed, Farid; Tajaddini, Azita; Heyouni, Mohammed; Elbouyahyaoui, Lakhdar

doi:10.1016/j.apnum.2021.10.020

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Cited by 6 publications

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“…The rapid and efficient techniques of solution-finding for multilinear systems [1][2][3][4][5][6]) are becoming increasingly significant in the field of science and engineering due to their extensive applications. In particular, some approaches with respect to higher order tensors [7][8][9][10][11][12][13][14][15] for data analysis have been widely studied in the era of Big Data.…”

Section: Introductionmentioning

confidence: 99%

Efficient Splitting Methods for Solving Tensor Absolute Value Equation

2022

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The tensor absolute value equation is a class of interesting structured multilinear systems. In this article, from the perspective of pure numerical algebra, we first consider a tensor-type successive over-relaxation method (SOR) (called TSOR) and tensor-type accelerated over-relaxation method (AOR) (called TAOR) for solving tensor absolute value equations. Furthermore, one type of preconditioned tensor splitting method is also applied for solving structured multilinear systems. Numerical experiments adequately demonstrate the efficiency of the presented methods.

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