Completion problems of partial $ N_0^1 $-matrices under directed 2-trees

Gu-Fang Mou; Gu-Fang Mou

doi:10.3934/math.2025417

AIMS Mathematics

2025, Volume 10, Issue 4: 9055-9072. doi: 10.3934/math.2025417

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Research article

Completion problems of partial $ N_0^1 $-matrices under directed 2-trees

Gu-Fang Mou ^,

College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan, China

Received: 23 January 2025 Revised: 24 March 2025 Accepted: 02 April 2025 Published: 21 April 2025
MSC : 05C22, 05C50, 15A48, 15A57

A matrix completion problem asks whether a partial matrix has a completion to a conventional matrix with a desired property. C. Mendes Ara$ \acute {u} $jo and J. R. Torregrosa explored the completion problem of a combinatorially symmetric N0-matrix by applying an undirected graph. However, in practical applications such as seismic data reconstruction, data transmission, and engineering computation data are often incomplete and must be represented by a non-combinatorially symmetric matrix. In this paper, we discuss the completion problem of a non-combinatorially symmetric partial matrix by using a directed graph and prove that a non-combinatorially symmetric partial matrix under a directed 2-tree is completed as an $ N_0^1 $-matrix.
- partial matrix,
- matrix completion,
- $ N_0^1 $-matrix,
- directed 2-tree
Citation: Gu-Fang Mou. Completion problems of partial $ N_0^1 $-matrices under directed 2-trees[J]. AIMS Mathematics, 2025, 10(4): 9055-9072. doi: 10.3934/math.2025417

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Abstract

A matrix completion problem asks whether a partial matrix has a completion to a conventional matrix with a desired property. C. Mendes Ara$ \acute {u} $jo and J. R. Torregrosa explored the completion problem of a combinatorially symmetric N0-matrix by applying an undirected graph. However, in practical applications such as seismic data reconstruction, data transmission, and engineering computation data are often incomplete and must be represented by a non-combinatorially symmetric matrix. In this paper, we discuss the completion problem of a non-combinatorially symmetric partial matrix by using a directed graph and prove that a non-combinatorially symmetric partial matrix under a directed 2-tree is completed as an $ N_0^1 $-matrix.

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