M-positive semi-definiteness and M-positive definiteness of fourth-order partially symmetric Cauchy tensors

Autor: Haitao Che, Haibin Chen, Yiju Wang
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Journal of Inequalities and Applications, Vol 2019, Iss 1, Pp 1-18 (2019)
Druh dokumentu: article
ISSN: 1029-242X
DOI: 10.1186/s13660-019-1986-x
Popis: Abstract Inspired by symmetric Cauchy tensors, we define fourth-order partially symmetric Cauchy tensors with their generating vectors. In this article, we focus on the necessary and sufficient conditions for the M-positive semi-definiteness and M-positive definiteness of fourth-order Cauchy tensors. Moreover, the necessary and sufficient conditions of the strong ellipticity conditions for fourth-order Cauchy tensors are obtained. Furthermore, fourth-order Cauchy tensors are M-positive semi-definite if and only if the homogeneous polynomial for fourth-order Cauchy tensors is monotonically increasing. Several M-eigenvalue inclusion theorems and spectral properties of fourth-order Cauchy tensors are discussed. A power method is proposed to compute the smallest and the largest M-eigenvalues of fourth-order Cauchy tensors. The given numerical experiments show the effectiveness of the proposed method.
Databáze: Directory of Open Access Journals
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