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

研究成果: Article査読

15 被引用数 (Scopus)

抄録

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 chordal-structured matrix due to Grone, Johnson, Sá, 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.

本文言語English
ページ(範囲)819-823
ページ数5
ジャーナルLinear Algebra and Its Applications
433
4
DOI
出版ステータスPublished - 2010 10月 1
外部発表はい

ASJC Scopus subject areas

  • 代数と数論
  • 数値解析
  • 幾何学とトポロジー
  • 離散数学と組合せ数学

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