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Finding a low-rank basis in a matrix subspace

Abstract:

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained by the tensor CP decomposition. For the higher rank case, the situation is not as straightforward. In this work we present an algorithm based on a greedy process applicable to higher rank problems. Our algorithm first estimates the minimum rank by applying ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s10107-016-1042-2

Authors


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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Christ Church
Role:
Author
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Role:
Author
ORCID:
0000-0001-9519-2487
Publisher:
Springer Verlag
Journal:
Mathematical Programming More from this journal
Volume:
162
Issue:
1-2
Pages:
325–361
Publication date:
2016-06-29
Acceptance date:
2016-06-14
DOI:
EISSN:
1436-4646
ISSN:
0025-5610
Language:
English
Keywords:
Pubs id:
pubs:993757
UUID:
uuid:f4079a45-2be7-4240-a5fb-3cb13a4b770f
Local pid:
pubs:993757
Source identifiers:
993757
Deposit date:
2019-04-23

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