Two-step parameterized tensor-based iterative methods for solving $\mathcal{A}_{*M}\mathcal{X}_{*M}\mathcal{B}=\mathcal{C}$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916600598233088 |
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| author | Behera, Ratikanta Panda, Saroja Kumar Sahoo, Jajati Keshari |
| author_facet | Behera, Ratikanta Panda, Saroja Kumar Sahoo, Jajati Keshari |
| contents | Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the tensor equations $\mathcal{A}_{*M}\mathcal{X}_{*M}\mathcal{B}=\mathcal{C}$ by incorporating preconditioning techniques and parametric optimization to enhance convergence properties. The theoretical results were complemented by comprehensive numerical experiments that demonstrated the computational efficiency of the proposed two-step parametrized iterative methods. The convergence criterion for parameter selection has been studied and a few numerical experiments have been conducted for optimal parameter selection. Effective algorithms were proposed to compute iterative methods based on two-step parameterized tensors, and the results are promising. In addition, we discuss the solution of the Sylvester equations and a regularized least-squares solution for image deblurring problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_03921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-step parameterized tensor-based iterative methods for solving $\mathcal{A}_{*M}\mathcal{X}_{*M}\mathcal{B}=\mathcal{C}$ Behera, Ratikanta Panda, Saroja Kumar Sahoo, Jajati Keshari Numerical Analysis Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the tensor equations $\mathcal{A}_{*M}\mathcal{X}_{*M}\mathcal{B}=\mathcal{C}$ by incorporating preconditioning techniques and parametric optimization to enhance convergence properties. The theoretical results were complemented by comprehensive numerical experiments that demonstrated the computational efficiency of the proposed two-step parametrized iterative methods. The convergence criterion for parameter selection has been studied and a few numerical experiments have been conducted for optimal parameter selection. Effective algorithms were proposed to compute iterative methods based on two-step parameterized tensors, and the results are promising. In addition, we discuss the solution of the Sylvester equations and a regularized least-squares solution for image deblurring problems. |
| title | Two-step parameterized tensor-based iterative methods for solving $\mathcal{A}_{*M}\mathcal{X}_{*M}\mathcal{B}=\mathcal{C}$ |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.03921 |