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arXiv · 2409.10282

Matrix Completion and Decomposition in Phase Bounded Cones

Ding Zhang·Axel Ringh·Li Qiu
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Abstract

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.

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Ding Zhang, Axel Ringh, Li Qiu. 2024-09-16. Matrix Completion and Decomposition in Phase Bounded Cones. https://doi.org/10.1137/23m1626529

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