Computation of tensors generalized inverses under $M$-product and applications
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916368471818240 |
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| author | Sahoo, Jajati Keshari Panda, Saroja Kumar Behera, Ratikanta Stanimirović, Predrag S. |
| author_facet | Sahoo, Jajati Keshari Panda, Saroja Kumar Behera, Ratikanta Stanimirović, Predrag S. |
| contents | This paper introduces notions of the Drazin and the core-EP inverses on tensors via M-product. We propose a few properties of the Drazin and core-EP inverses of tensors, as well as effective tensor-based algorithms for calculating these inverses. In addition, definitions of composite generalized inverses are presented in the framework of the M-product, including CMP, DMP, and MPD inverse of tensors. Tensor-based higher-order Gauss-Seidel and Gauss-Jacobi iterative methods are designed. Algorithms for these two iterative methods to solve multilinear equations are developed. Certain multilinear systems are solved using the Drazin inverse, core-EP inverses, and composite generalized inverses such as CMP, DMP, and MPD inverse. A tensor M-product-based regularization technique is applied to solve the color image deblurring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computation of tensors generalized inverses under $M$-product and applications Sahoo, Jajati Keshari Panda, Saroja Kumar Behera, Ratikanta Stanimirović, Predrag S. Numerical Analysis This paper introduces notions of the Drazin and the core-EP inverses on tensors via M-product. We propose a few properties of the Drazin and core-EP inverses of tensors, as well as effective tensor-based algorithms for calculating these inverses. In addition, definitions of composite generalized inverses are presented in the framework of the M-product, including CMP, DMP, and MPD inverse of tensors. Tensor-based higher-order Gauss-Seidel and Gauss-Jacobi iterative methods are designed. Algorithms for these two iterative methods to solve multilinear equations are developed. Certain multilinear systems are solved using the Drazin inverse, core-EP inverses, and composite generalized inverses such as CMP, DMP, and MPD inverse. A tensor M-product-based regularization technique is applied to solve the color image deblurring. |
| title | Computation of tensors generalized inverses under $M$-product and applications |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.16111 |