A metric function for dual quaternion matrices and related least-squares problems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912110903033856 |
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| author | Ling, Chen Pan, Chenjian Qi, Liqun |
| author_facet | Ling, Chen Pan, Chenjian Qi, Liqun |
| contents | Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate dual quaternion overdetermined equations as a least squares problem, which is further converted into a bi-level optimization problem. Numerically, we propose two implementable proximal point algorithms for finding approximate solutions of dual quaternion overdetermined equations. The relevant convergence theorems %and computational complexity estimates have also been established. Preliminary simulation results on synthetic and color image datasets demonstrate the effectiveness of the proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05306 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A metric function for dual quaternion matrices and related least-squares problems Ling, Chen Pan, Chenjian Qi, Liqun Optimization and Control Rings and Algebras Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate dual quaternion overdetermined equations as a least squares problem, which is further converted into a bi-level optimization problem. Numerically, we propose two implementable proximal point algorithms for finding approximate solutions of dual quaternion overdetermined equations. The relevant convergence theorems %and computational complexity estimates have also been established. Preliminary simulation results on synthetic and color image datasets demonstrate the effectiveness of the proposed algorithms. |
| title | A metric function for dual quaternion matrices and related least-squares problems |
| topic | Optimization and Control Rings and Algebras |
| url | https://arxiv.org/abs/2411.05306 |