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A New Algorithm for Positive Semidefinite Matrix Completion
"... Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and lowrank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control. This task can be conducted by solving the nuclear norm regularized ..."
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Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and lowrank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control. This task can be conducted by solving the nuclear norm
Positive semidefinite matrix completions on chordal graphs and the constraint nondegeneracy in semidefinite programming
, 2008
"... LetG = (V,E) be a graph. In matrix completion theory, it is known that the following two conditions are equivalent: (i) G is a chordal graph; (ii) Every Gpartial positive semidefinite matrix has a positive semidefinite matrix completion. In this paper, we relate these two conditions to constraint n ..."
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Cited by 4 (0 self)
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LetG = (V,E) be a graph. In matrix completion theory, it is known that the following two conditions are equivalent: (i) G is a chordal graph; (ii) Every Gpartial positive semidefinite matrix has a positive semidefinite matrix completion. In this paper, we relate these two conditions to constraint
ZONAL POLYNOMIALS OF POSITIVE SEMIDEFINITE MATRIX ARGUMENT
, 2004
"... By using the linear structure theory of Magnus (12), this work proposes an alternative way to James (11) for obtaining the LaplaceBeltrami operator, who has the zonal polynomials of positive definite matrix argument as eigenfunctions, in particular, an explicit expression for the matrix G(v(X)), ..."
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theory of James (11) a differential metric depending on the MoorePenrose inverse is proposed for the space of m×m positive semidefinite matrices. As in the definite case, the LaplaceBeltrami operator for the calculation of zonal polynomials of positive semidefinite matrix argument is derived. In a
Complexity of the positive semidefinite matrix completion problem with a rank constraint
, 2014
"... We consider the decision problem asking whether a partial rational symmetric matrix with an allones diagonal can be completed to a full positive semidefinite matrix of rank at most k. We show that this problem is NPhard for any fixed integer k ≥ 2. Equivalently, for k ≥ 2, it is NPhard to test me ..."
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Cited by 3 (3 self)
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We consider the decision problem asking whether a partial rational symmetric matrix with an allones diagonal can be completed to a full positive semidefinite matrix of rank at most k. We show that this problem is NPhard for any fixed integer k ≥ 2. Equivalently, for k ≥ 2, it is NPhard to test
Positive Semidefinite Matrix Completion, Universal Rigidity and the Strong Arnold Property
, 2013
"... This paper addresses the following three topics: positive semidefinite (psd) matrix completions, universal rigidity of frameworks, and the Strong Arnold Property (SAP). We show some strong connections among these topics, using semidefinite programming as unifying theme. Our main contribution is a su ..."
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Cited by 4 (1 self)
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This paper addresses the following three topics: positive semidefinite (psd) matrix completions, universal rigidity of frameworks, and the Strong Arnold Property (SAP). We show some strong connections among these topics, using semidefinite programming as unifying theme. Our main contribution is a
Complexity of the positive semidefinite matrix completion problem with a rank constraint
, 2012
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SERIES B: Operations ResearchExploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion
, 2009
"... Abstract. A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear or ..."
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Abstract. A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear
Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion
, 2010
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Tokyo Institute of Technology SERIES B: Operations ResearchExploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion
, 2009
"... Abstract. A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear or ..."
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Abstract. A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear
A new graph parameter related to bounded rank positive semidefinite matrix completions
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Results 1  10
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