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...
Ausführliche Beschreibung
Autor*in: |
Xiaohan Li [verfasserIn] Xin Liu [verfasserIn] Jing Jiang [verfasserIn] Jian Sun [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2023 |
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Übergeordnetes Werk: |
In: AIMS Mathematics - AIMS Press, 2018, 8(2023), 11, Seite 27725-27741 |
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Übergeordnetes Werk: |
volume:8 ; year:2023 ; number:11 ; pages:27725-27741 |
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DOI / URN: |
10.3934/math.20231419 |
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Katalog-ID: |
DOAJ100771181 |
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10.3934/math.20231419 doi (DE-627)DOAJ100771181 (DE-599)DOAJ6ee932c4af3b4f2f9039bafcbb475516 DE-627 ger DE-627 rakwb eng QA1-939 Xiaohan Li verfasserin aut Some solutions to a third-order quaternion tensor equation 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. tensor equation qt-product generalized inverse quaternion matrix least-squares solution minimum-norm solution Mathematics Xin Liu verfasserin aut Jing Jiang verfasserin aut Jian Sun verfasserin aut In AIMS Mathematics AIMS Press, 2018 8(2023), 11, Seite 27725-27741 (DE-627)1011276194 (DE-600)2917342-5 24736988 nnns volume:8 year:2023 number:11 pages:27725-27741 https://doi.org/10.3934/math.20231419 kostenfrei https://doaj.org/article/6ee932c4af3b4f2f9039bafcbb475516 kostenfrei https://www.aimspress.com/article/doi/10.3934/math.20231419?viewType=HTML kostenfrei https://doaj.org/toc/2473-6988 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2023 11 27725-27741 |
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10.3934/math.20231419 doi (DE-627)DOAJ100771181 (DE-599)DOAJ6ee932c4af3b4f2f9039bafcbb475516 DE-627 ger DE-627 rakwb eng QA1-939 Xiaohan Li verfasserin aut Some solutions to a third-order quaternion tensor equation 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. tensor equation qt-product generalized inverse quaternion matrix least-squares solution minimum-norm solution Mathematics Xin Liu verfasserin aut Jing Jiang verfasserin aut Jian Sun verfasserin aut In AIMS Mathematics AIMS Press, 2018 8(2023), 11, Seite 27725-27741 (DE-627)1011276194 (DE-600)2917342-5 24736988 nnns volume:8 year:2023 number:11 pages:27725-27741 https://doi.org/10.3934/math.20231419 kostenfrei https://doaj.org/article/6ee932c4af3b4f2f9039bafcbb475516 kostenfrei https://www.aimspress.com/article/doi/10.3934/math.20231419?viewType=HTML kostenfrei https://doaj.org/toc/2473-6988 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2023 11 27725-27741 |
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10.3934/math.20231419 doi (DE-627)DOAJ100771181 (DE-599)DOAJ6ee932c4af3b4f2f9039bafcbb475516 DE-627 ger DE-627 rakwb eng QA1-939 Xiaohan Li verfasserin aut Some solutions to a third-order quaternion tensor equation 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. tensor equation qt-product generalized inverse quaternion matrix least-squares solution minimum-norm solution Mathematics Xin Liu verfasserin aut Jing Jiang verfasserin aut Jian Sun verfasserin aut In AIMS Mathematics AIMS Press, 2018 8(2023), 11, Seite 27725-27741 (DE-627)1011276194 (DE-600)2917342-5 24736988 nnns volume:8 year:2023 number:11 pages:27725-27741 https://doi.org/10.3934/math.20231419 kostenfrei https://doaj.org/article/6ee932c4af3b4f2f9039bafcbb475516 kostenfrei https://www.aimspress.com/article/doi/10.3934/math.20231419?viewType=HTML kostenfrei https://doaj.org/toc/2473-6988 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2023 11 27725-27741 |
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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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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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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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score |
7.4004526 |