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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.10282 |
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| _version_ | 1866913959409352704 |
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| author | Zhang, Ding Ringh, Axel Qiu, Li |
| author_facet | Zhang, Ding Ringh, Axel Qiu, Li |
| contents | The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This paper considers the completion and decomposition problems in a broader class of cones, namely phase-bounded cones. We show that most of the main results from the PSD case carry over to the phase-bounded case. More precisely, this is done by first unveiling a duality between the completion and decomposition problems, using a dual cone interpretation. Based on this, we then derive necessary and sufficient conditions for the phase-bounded completion and decomposition problems, and also characterize all phase-bounded completions of a completable partial matrix with a banded pattern. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10282 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matrix Completion and Decomposition in Phase Bounded Cones Zhang, Ding Ringh, Axel Qiu, Li Optimization and Control Systems and Control Rings and Algebras The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This paper considers the completion and decomposition problems in a broader class of cones, namely phase-bounded cones. We show that most of the main results from the PSD case carry over to the phase-bounded case. More precisely, this is done by first unveiling a duality between the completion and decomposition problems, using a dual cone interpretation. Based on this, we then derive necessary and sufficient conditions for the phase-bounded completion and decomposition problems, and also characterize all phase-bounded completions of a completable partial matrix with a banded pattern. |
| title | Matrix Completion and Decomposition in Phase Bounded Cones |
| topic | Optimization and Control Systems and Control Rings and Algebras |
| url | https://arxiv.org/abs/2409.10282 |