Matrix Completion and Decomposition in Phase Bounded Cones
<|reference_start|>Matrix Completion and Decomposition in Phase Bounded Cones: 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.<|reference_end|>
@article{zhang2024matrix,
    title={Matrix Completion and Decomposition in Phase Bounded Cones},
    author={Ding Zhang, Axel Ringh, Li Qiu},
    journal={arXiv preprint arXiv:2409.10282},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.10282},
    primaryClass={math.OC cs.SY eess.SY math.RA}
}