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A direct proof for the matrix decomposition of chordal-structured positive semidefinite matrices

โœ Scribed by Naonori Kakimura

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
116 KB
Volume
433
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Agler, Helton, McCullough, and Rodman proved that a graph is chordal if and only if any positive semidefinite (PSD) symmetric matrix, whose nonzero entries are specified by a given graph, can be decomposed as a sum of PSD matrices corresponding to the maximal cliques. This decomposition is recently exploited to solve positive semidefinite programming efficiently. Their proof is based on a characterization for PSD matrix completion of a chordalstructured matrix due to Grone, Johnson, S รก, and Wolkowicz. This note gives a direct and simpler proof for the result of Agler et al., which leads to an alternative proof of Grone et al.

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