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A New Algorithm for Positive Semidefinite Matrix Completion [PDF]
Journal of Applied Mathematics, 2016 Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and low-rank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control.
Fangfang Xu, Peng Pan
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Norm inequalities for functions of matrices [PDF]
HeliyonIn this paper, we prove several spectral norm and unitarily invariant norm inequalities for matrices in which the special cases of our results present some known inequalities. Also, some of our results give interpolating inequalities which are related to
Ahmad Al-Natoor
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Low-rank matrix approximations over canonical subspaces
Journal of Numerical Analysis and Approximation Theory, 2020 In this paper we derive closed form expressions for the nearest rank-\(k\) matrix on canonical subspaces. We start by studying three kinds of subspaces. Let \(X\) and \(Y\) be a pair of given matrices. The first subspace contains all the \(m\times
Achiya Dax
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Some upper and lower bounds on PSD-rank [PDF]
, 2014 Positive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for showing lower bounds
de Wolf, Ronald, Lee, Troy, Wei, Zhaohui
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Hilbert’s 17th problem in free skew fields
Forum of Mathematics, Sigma, 2020 This paper solves the rational noncommutative analogue of Hilbert’s 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of Hermitian matrices in its domain, then it is a sum of Hermitian squares of noncommutative ...
Jurij Volčič
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Analysis of Fixing Nodes Used in Generalized Inverse Computation
Advances in Electrical and Electronic Engineering, 2014 In various fields of numerical mathematics, there arises the need to compute a generalized inverse of a symmetric positive semidefinite matrix, for example in the solution of contact problems.
Pavla Hruskova
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The complete positivity of symmetric tridiagonal and pentadiagonal matrices
Special Matrices, 2022 We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix AA is completely positive. Our decomposition can be applied to a wide range of matrices.
Cao Lei, McLaren Darian, Plosker Sarah
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A Semidefinite Hierarchy for Containment of Spectrahedra [PDF]
, 2015 A spectrahedron is the positivity region of a linear matrix pencil and thus the feasible set of a semidefinite program. We propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in another one ...
Kellner, Kai +2 more
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Sufficient conditions to be exceptional
Special Matrices, 2016 A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A
Johnson Charles R., Reams Robert B.
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Distance Matrix of a Class of Completely Positive Graphs: Determinant and Inverse
Special Matrices, 2020 A real symmetric matrix A is said to be completely positive if it can be written as BBt for some (not necessarily square) nonnegative matrix B. A simple graph G is called a completely positive graph if every matrix realization of G that is both ...
Das Joyentanuj +2 more
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