Linear homotopy method for computing generalized tensor eigenpairs

Liping CHEN; Lixing HAN; Liangmin ZHOU

doi:10.1007/s11464-017-0662-z

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Front. Math. China ›› 2017, Vol. 12 ›› Issue (6) : 1303-1317. DOI: 10.1007/s11464-017-0662-z

RESEARCH ARTICLE

Linear homotopy method for computing generalized tensor eigenpairs

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Abstract

Let m, $m ′$ , n be positive integers such that $m ≠ m ′$ . Let $A$ be an mth order n-dimensional tensor, and let $B$ be an $m ′$ th order n-dimensional tensor. λ ∈ $ℂ$ is called a $B$ -eigenvalue of $A$ if $A x m − 1 = λ B x m ′ − 1$ and $B x m ′ = 1$ for some x ∈ $ℂ n \ {0}$ . In this paper, we propose a linear homotopy method for solving this eigenproblem. We prove that the method finds all isolated $B$ -eigenpairs. Moreover, it is easy to implement. Numerical results are provided to show the efficiency of the proposed method.

Keywords

Tensors / generalized eigenpairs / polynomial systems / linear homotopy

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Liping CHEN, Lixing HAN, Liangmin ZHOU. Linear homotopy method for computing generalized tensor eigenpairs. Front. Math. China, 2017, 12(6): 1303‒1317 https://doi.org/10.1007/s11464-017-0662-z

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