Continuation methods for computing Z-/H-eigenpairs of nonnegative tensors

Yueh Cheng Kuo; Wen-Wei Lin; Ching Sung Liu

doi:10.1016/j.cam.2018.02.027

Continuation methods for computing Z-/H-eigenpairs of nonnegative tensors

Yueh Cheng Kuo, Wen-Wei Lin, Ching Sung Liu^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.

Original language	English
Pages (from-to)	71-88
Number of pages	18
Journal	Journal of Computational and Applied Mathematics
Volume	340
DOIs	https://doi.org/10.1016/j.cam.2018.02.027
State	Published - 1 Oct 2018

Keywords

Continuation method
H-eigenpair
Nonnegative tensor
Tensor eigenvalue problem
Z-eigenpair

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title = "Continuation methods for computing Z-/H-eigenpairs of nonnegative tensors",

abstract = "In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.",

keywords = "Continuation method, H-eigenpair, Nonnegative tensor, Tensor eigenvalue problem, Z-eigenpair",

author = "Kuo, {Yueh Cheng} and Wen-Wei Lin and Liu, {Ching Sung}",

year = "2018",

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doi = "10.1016/j.cam.2018.02.027",

language = "English",

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AU - Kuo, Yueh Cheng

AU - Lin, Wen-Wei

AU - Liu, Ching Sung

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Y1 - 2018/10/1

N2 - In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.

AB - In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.

KW - Continuation method

KW - H-eigenpair

KW - Nonnegative tensor

KW - Tensor eigenvalue problem

KW - Z-eigenpair

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SP - 71

EP - 88

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

Continuation methods for computing Z-/H-eigenpairs of nonnegative tensors

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Keywords

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