Linear homotopy method for computing generalized tensor eigenpairs

doi:10.1007/s11464-017-0662-z

Front. Math. China

2017, Vol. 12

Issue (6) : 1303-1317 https://doi.org/10.1007/s11464-017-0662-z

RESEARCH ARTICLE

Linear homotopy method for computing generalized tensor eigenpairs

Liping CHEN¹, Lixing HAN²(

), Liangmin ZHOU¹

¹. Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
². Department of Mathematics, University of Michigan-Flint, Flint, MI 48502, USA

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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 ∈ $?$ 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 ∈ $? n \ {0}$ . 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

Corresponding Author(s): Lixing HAN

Issue Date: 27 November 2017

Cite this article:

Liping CHEN,Lixing HAN,Liangmin ZHOU. Linear homotopy method for computing generalized tensor eigenpairs[J]. Front. Math. China, 2017, 12(6): 1303-1317.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0662-z
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I6/1303

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