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

DOI10.1016/j.laa.2010.04.012zbMath1196.15026OpenAlexW1978613254MaRDI QIDQ979016

Naonori Kakimura

Publication date: 25 June 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.04.012

zbMATH Keywords

rankchordal graphspositive semidefinite matricesmatrix completion problem

Mathematics Subject Classification ID

Factorization of matrices (15A23) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48) Vector spaces, linear dependence, rank, lineability (15A03) Matrix completion problems (15A83)

Related Items (6)

Matrices attaining the minimum semidefinite rank of a chordal graph ⋮ Sparse polynomial optimisation for neural network verification ⋮ Sum-of-squares chordal decomposition of polynomial matrix inequalities ⋮ Decomposition of arrow type positive semidefinite matrices with application to topology optimization ⋮ Chordal decomposition in operator-splitting methods for sparse semidefinite programs ⋮ Decomposed structured subsets for semidefinite and sum-of-squares optimization

Cites Work

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• Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion
• Positive definite completions of partial Hermitian matrices
• Positive semidefinite matrices with a given sparsity pattern
• Cuts, matrix completions and graph rigidity
• On the sparsity order of a graph and its deficiency in chordality

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