Positive definite completions and determinant maximization

DOI10.1016/S0024-3795(98)10211-2zbMath0973.15009MaRDI QIDQ1300861

Charles R. Johnson, Pablo Tarazaga, Thomas L. Hayden, William Glunt

Publication date: 3 December 2001

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

zbMATH Keywords

algorithmglobal convergenceHermitian matrixpartial matrixdeterminant maximizing completionpositive definite completion

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Inverse problems in linear algebra (15A29) Positive matrices and their generalizations; cones of matrices (15B48) Numerical computation of determinants (65F40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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Connections between the real positive semidefinite and distance matrix completion problems, An efficient algorithm for maximum entropy extension of block-circulant covariance matrices, Geometric mean of partial positive definite matrices with missing entries, Semidefinite programming for discrete optimization and matrix completion problems, Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming, A maximum entropy approach to the realizability of spin correlation matrices

Cites Work

• Positive definite completions of partial Hermitian matrices
• Gaussian Markov distributions over finite graphs
• Spanning-tree extensions of the Hadamard-Fischer inequalities
• Bounded groups and norm-Hermitian matrices
• Determinantal formulae for matrix completions associated with chordal graphs
• Matrix Analysis
• The Euclidian Distance Matrix Completion Problem
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