Some solutions to a third-order quaternion tensor equation

The paper deals with the third-order quaternion tensor equation. Based on the Qt multiplication operation, we derive solvability conditions and also get the general solution, the least-squares solution, the minimum-norm solution and the minimum-norm least-squares solution of the tensor equation $ \m...
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Autor*in:	Xiaohan Li [verfasserIn] Xin Liu [verfasserIn] Jing Jiang [verfasserIn] Jian Sun [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	tensor equation qt-product generalized inverse quaternion matrix least-squares solution minimum-norm solution

Übergeordnetes Werk:	In: AIMS Mathematics - AIMS Press, 2018, 8(2023), 11, Seite 27725-27741
Übergeordnetes Werk:	volume:8 ; year:2023 ; number:11 ; pages:27725-27741

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3934/math.20231419

Katalog-ID:	DOAJ100771181

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source	In AIMS Mathematics 8(2023), 11, Seite 27725-27741 volume:8 year:2023 number:11 pages:27725-27741
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topic_facet	tensor equation qt-product generalized inverse quaternion matrix least-squares solution minimum-norm solution Mathematics
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callnumber-first	Q - Science
author	Xiaohan Li
spellingShingle	Xiaohan Li misc QA1-939 misc tensor equation misc qt-product misc generalized inverse misc quaternion matrix misc least-squares solution misc minimum-norm solution misc Mathematics Some solutions to a third-order quaternion tensor equation
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topic_title	QA1-939 Some solutions to a third-order quaternion tensor equation tensor equation qt-product generalized inverse quaternion matrix least-squares solution minimum-norm solution
topic	misc QA1-939 misc tensor equation misc qt-product misc generalized inverse misc quaternion matrix misc least-squares solution misc minimum-norm solution misc Mathematics
topic_unstemmed	misc QA1-939 misc tensor equation misc qt-product misc generalized inverse misc quaternion matrix misc least-squares solution misc minimum-norm solution misc Mathematics
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title	Some solutions to a third-order quaternion tensor equation
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title_full	Some solutions to a third-order quaternion tensor equation
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title_sort	some solutions to a third-order quaternion tensor equation
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title_auth	Some solutions to a third-order quaternion tensor equation
abstract	The paper deals with the third-order quaternion tensor equation. Based on the Qt multiplication operation, we derive solvability conditions and also get the general solution, the least-squares solution, the minimum-norm solution and the minimum-norm least-squares solution of the tensor equation $ \mathcal{A} \ast_{\mathbb{Q}} \mathcal{X} = \mathcal{B} $. Finally, two numerical examples are presented.
abstractGer	The paper deals with the third-order quaternion tensor equation. Based on the Qt multiplication operation, we derive solvability conditions and also get the general solution, the least-squares solution, the minimum-norm solution and the minimum-norm least-squares solution of the tensor equation $ \mathcal{A} \ast_{\mathbb{Q}} \mathcal{X} = \mathcal{B} $. Finally, two numerical examples are presented.
abstract_unstemmed	The paper deals with the third-order quaternion tensor equation. Based on the Qt multiplication operation, we derive solvability conditions and also get the general solution, the least-squares solution, the minimum-norm solution and the minimum-norm least-squares solution of the tensor equation $ \mathcal{A} \ast_{\mathbb{Q}} \mathcal{X} = \mathcal{B} $. Finally, two numerical examples are presented.
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title_short	Some solutions to a third-order quaternion tensor equation
url	https://doi.org/10.3934/math.20231419 https://doaj.org/article/6ee932c4af3b4f2f9039bafcbb475516 https://www.aimspress.com/article/doi/10.3934/math.20231419?viewType=HTML https://doaj.org/toc/2473-6988
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up_date	2024-07-03T16:35:33.902Z
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