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Decomposition and completion of sum-of-squares matrices

Abstract:

This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices that are nonzero only on a principal submatrix. Also, the completion of an SOS matrix is equivalent to a set of SOS conditions on its principal submatrices and a consistency condition on the Gram representation of the principal submatrices. These results ar...

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Publication status:
Not published
Peer review status:
Not peer reviewed

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Oxford college:
Worcester College
Role:
Author
ORCID:
0000-0002-3565-8967
University of Oxford More from this funder
Journal:
CoRR
Publication date:
2018-01-01
Pubs id:
pubs:847962
URN:
uri:c589b740-832c-47d3-aa2e-f1f14f9ed46b
UUID:
uuid:c589b740-832c-47d3-aa2e-f1f14f9ed46b
Local pid:
pubs:847962

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