On the extensions of the GD inverse of tensors via the M-Product
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917861332615168 |
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| author | Jin, Hongwei Chen, Siran Huang, Shaowu Stanimirović, Predrag S. |
| author_facet | Jin, Hongwei Chen, Siran Huang, Shaowu Stanimirović, Predrag S. |
| contents | We study extensions of the GD tensor inverse using the M-product. The aim of current research is threefold. In the first place, the tensor GD inverse under the M-product is introduced and considered. We give the several properties and representations of the GD inverse using the core nilpotent decomposition and then establish the reverse-order law rules for the GD inverse. Second, the tensor GDMP inverse is studied and the corresponding numerical algorithm is given. In addition, the reverse- and forward-order laws of the GDMP inverse are established. Third, the GD-Star tensor inverse under the M-product is introduced and studied. Finally, the GD inverse, GDMP inverse and GD-Star inverse solutions of multilinear equations are investigated. Illustrative numerical calculation is performed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05799 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the extensions of the GD inverse of tensors via the M-Product Jin, Hongwei Chen, Siran Huang, Shaowu Stanimirović, Predrag S. Numerical Analysis Mathematical Physics We study extensions of the GD tensor inverse using the M-product. The aim of current research is threefold. In the first place, the tensor GD inverse under the M-product is introduced and considered. We give the several properties and representations of the GD inverse using the core nilpotent decomposition and then establish the reverse-order law rules for the GD inverse. Second, the tensor GDMP inverse is studied and the corresponding numerical algorithm is given. In addition, the reverse- and forward-order laws of the GDMP inverse are established. Third, the GD-Star tensor inverse under the M-product is introduced and studied. Finally, the GD inverse, GDMP inverse and GD-Star inverse solutions of multilinear equations are investigated. Illustrative numerical calculation is performed. |
| title | On the extensions of the GD inverse of tensors via the M-Product |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2412.05799 |