Autor: |
Haitao Che, Haibin Chen, Yiju Wang |
Jazyk: |
angličtina |
Rok vydání: |
2019 |
Předmět: |
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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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