Frontiers of Mathematics in China >

2017 , Vol. 12 >Issue 6: 1303 - 1317

DOI: https://doi.org/10.1007/s11464-017-0662-z

RESEARCH ARTICLE

Linear homotopy method for computing generalized tensor eigenpairs

  • Liping CHEN 1 ,
  • Lixing HAN , 2 ,
  • Liangmin ZHOU 1
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  • 1. Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
  • 2. Department of Mathematics, University of Michigan-Flint, Flint, MI 48502, USA

Received date: 24 Jul 2015

Accepted date: 21 Sep 2017

Published date: 27 Nov 2017

Copyright

2017 Higher Education Press and Springer-Verlag GmbH Germany
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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 Axm−1=λBxm′−1 and Bxm′=1 for some x ∈ℂn\{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.

Key words： Tensors; generalized eigenpairs; polynomial systems; linear homotopy

Cite this article

Liping CHEN , Lixing HAN , Liangmin ZHOU . Linear homotopy method for computing generalized tensor eigenpairs[J]. Frontiers of Mathematics in China, 2017 , 12(6) : 1303 -1317 . DOI: 10.1007/s11464-017-0662-z

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