Results 11 to 20 of about 49,656 (213)
Generalized low-rank approximation to the symmetric positive semidefinite matrix
AIMS MathematicsIn this paper, we consider the generalized low-rank approximation to the symmetric positive semidefinite matrix in the Frobenius norm: $ \underset{X}{\min} \sum^{m}_{i = 1}\left \Vert A_{i}-B_{i}XB_{i}^{T}\right \Vert^{2}_{F}, $ where $ X $ is an unknown
Haixia Chang, Chunmei Li, Longsheng Liu
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Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix [PDF]
, 2017 We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is ...
A Neumaier +30 more
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On (conditional) positive semidefiniteness in a matrix-valued context [PDF]
Studia Mathematica, 2017 In a nutshell, we intend to extend Schoenberg's classical theorem connecting conditionally positive semidefinite functions $F\colon \mathbb{R}^n \to \mathbb{C}$, $n \in \mathbb{N}$, and their positive semidefinite exponentials $\exp(tF)$, $t > 0$, to the
Gesztesy, Fritz, Pang, Michael
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Positive semidefinite univariate matrix polynomials [PDF]
Mathematische Zeitschrift, 2018 We study sum-of-squares representations of symmetric univariate real matrix polynomials that are positive semidefinite along the real line. We give a new proof of the fact that every positive semidefinite univariate matrix polynomial of size $n\times n$ can be written as a sum of squares $M=Q^TQ$, where $Q$ has size $(n+1)\times n$, which was recently ...
Hanselka, C., Sinn, R.
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Matrix Pencils with Coefficients that have Positive Semidefinite Hermitian Parts
SIAM Journal on Matrix Analysis and Applications, 2022 We analyze when an arbitrary matrix pencil is equivalent to a dissipative Hamiltonian pencil and show that this heavily restricts the spectral properties. In order to relax the spectral properties, we introduce matrix pencils with coefficients that have positive semidefinite Hermitian parts. We will make a detailed analysis of their spectral properties
C. Mehl, V. Mehrmann, M. Wojtylak
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Positive Semidefinite Matrix Factorization Based on Truncated Wirtinger Flow [PDF]
2020 28th European Signal Processing Conference (EUSIPCO), 2021 This paper deals with algorithms for positive semidefinite matrix factorization (PSDMF). PSDMF is a recently-proposed extension of nonnegative matrix factorization with applications in combinatorial optimization, among others. In this paper, we focus on improving the local convergence of an alternating block gradient (ABC) method for PSDMF in a noise ...
Lahat, Dana, Févotte, Cédric
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The Complexity of Positive Semidefinite Matrix Factorization [PDF]
SIAM Journal on Optimization, 2017 11 ...
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Singularity Degree of the Positive Semidefinite Matrix Completion Problem [PDF]
SIAM Journal on Optimization, 2017 The singularity degree of a semidefinite programming problem is the smallest number of facial reduction steps to make the problem strictly feasible. We introduce two new graph parameters, called the singularity degree and the nondegenerate singularity degree, based on the singularity degree of the positive semidefinite matrix completion problem.
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A trace bound for integer-diagonal positive semidefinite matrices
Special Matrices, 2020 We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.
Mitchell Lon
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On the closure of the completely positive semidefinite cone and linear approximations to quantum colorings [PDF]
, 2015 We investigate structural properties of the completely positive semidefinite cone $\mathcal{CS}_+^n$, consisting of all the $n \times n$ symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This cone has been
Burgdorf, Sabine +2 more
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