Functions preserving positive definiteness for sparse matrices

DOI10.1090/S0002-9947-2014-06183-7zbMath1305.15075arXiv1210.3894MaRDI QIDQ5496595

Dominique Guillot, Bala Rajaratnam

Publication date: 2 February 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.3894

zbMATH Keywords

positive definitenesssparse matricesgraphstreesabsolutely monotonic functionshard-thresholdingsoft-thresholdingentrywise matrix functions

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48) Monotonic functions, generalizations (26A48)

Related Items (16)

An inequality for tensor product of positive operators and its applications ⋮ Matrix positivity preservers in fixed dimension. I ⋮ A sharp lower-tail bound for Gaussian maxima with application to bootstrap methods in high dimensions ⋮ Moment-sequence transforms ⋮ Continuity of positive nonlinear maps between $C^*$-algebras ⋮ Inequalities for generalized matrix function and inner product ⋮ Positive definite Hankel matrix completions and Hamburger moment completions ⋮ Positivity preservers forbidden to operate on diagonal blocks ⋮ Critical exponents of graphs ⋮ A panorama of positivity. II: Fixed dimension ⋮ Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity ⋮ The critical exponent: a novel graph invariant ⋮ Matrix positivity preservers in fixed dimension ⋮ Schur polynomials and matrix positivity preservers ⋮ Preserving positivity for matrices with sparsity constraints ⋮ Preserving positivity for rank-constrained matrices

Cites Work

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• A General Framework for Weighted Gene Co-Expression Network Analysis

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