On computing minimal <i>H</i>-eigenvalue of sign-structured tensors

doi:10.1007/s11464-017-0645-0

Front. Math. China

2017, Vol. 12

Issue (6) : 1289-1302 https://doi.org/10.1007/s11464-017-0645-0

RESEARCH ARTICLE

On computing minimal H-eigenvalue of sign-structured tensors

Haibin CHEN(

), Yiju WANG

School of Management Science, Qufu Normal University, Rizhao 276826, China

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Abstract

Finding the minimal H-eigenvalue of tensors is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a sum-of-squares (SOS) algorithm for computing the minimal H-eigenvalues of tensors with some sign structures called extended essentially nonnegative tensors (EEN-tensors), which includes nonnegative tensors as a subclass. In the even-order symmetric case, we first discuss the positive semi-definiteness of EEN-tensors, and show that a positive semi-definite EEN-tensor is a nonnegative tensor or an M-tensor or the sum of a nonnegative tensor and an M-tensor, then we establish a checkable sufficient condition for the SOS decomposition of EEN-tensors. Finally, we present an efficient algorithm to compute the minimal H-eigenvalues of even-order symmetric EEN-tensors based on the SOS decomposition. Numerical experiments are given to show the efficiency of the proposed algorithm.

Keywords Extended essentially nonnegative tensor (EEN-tensor) positive semi-definiteness H-eigenvalue sum-of-squares (SOS) polynomial

Corresponding Author(s): Haibin CHEN

Issue Date: 27 November 2017

Cite this article:

Haibin CHEN,Yiju WANG. On computing minimal H-eigenvalue of sign-structured tensors[J]. Front. Math. China, 2017, 12(6): 1289-1302.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0645-0
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I6/1289

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