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Minimal rank completions for overlapping blocks

Epperly, Ethan N. and Govindarajan, Nithin and Chandrasekaran, Shivkumar (2021) Minimal rank completions for overlapping blocks. Linear Algebra and its Applications, 627 . pp. 185-198. ISSN 0024-3795. doi:10.1016/j.laa.2021.06.011. https://resolver.caltech.edu/CaltechAUTHORS:20210818-204746474

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Abstract

We consider the multi-objective optimization problem of choosing the bottom left block-entry of a block lower triangular matrix to minimize the ranks of all block sub-matrices. We provide a proof that there exists a simultaneous rank-minimizer by constructing the complete set of all minimizers.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.laa.2021.06.011DOIArticle
https://arxiv.org/abs/2106.11267arXivDiscussion Paper
ORCID:
AuthorORCID
Epperly, Ethan N.0000-0003-0712-8296
Additional Information:© 2021 Elsevier Inc. Received 24 January 2021, Accepted 16 June 2021, Available online 21 June 2021. We thank the anonymous reviewer for suggesting a significantly shorter and more revealing proof of Theorem 1 than the one we originally discovered, from which the proof presented in this article has been adapted. The authors have no competing interests to declare.
Subject Keywords:Matrix completion; Low-rank structure; Minimal rank completion
DOI:10.1016/j.laa.2021.06.011
Record Number:CaltechAUTHORS:20210818-204746474
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210818-204746474
Official Citation:Ethan N. Epperly, Nithin Govindarajan, Shivkumar Chandrasekaran, Minimal rank completions for overlapping blocks, Linear Algebra and its Applications, Volume 627, 2021, Pages 185-198, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2021.06.011.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110309
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Aug 2021 21:40
Last Modified:18 Aug 2021 21:40

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