Results 11 to 20 of about 6,682,316 (219)
Computing a nearest symmetric positive semidefinite matrix
Linear Algebra and its Applications, 1988 The problem of computing a nearest positive semidefinite matrix (notation used \(X\geq 0)\) to an arbitrary real matrix A is considered. The criterion of approximation is the distance \(\delta (A)=\min_{X=X^ T\geq 0}\| A-X\|\) where the norm is chosen to be either Frobenius or 2-norm. The paper consists of two parts. In the first part the author proves
Higham, Nicholas J.
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On the Positive Semidefinite Nature of a Certain Matrix Expression
Canadian Journal of Mathematics, 1964 By "positive definite matrices" or, briefly, definite matrices, we mean in this note self-adjoint matrices all the characteristic values of which are positive. Alternatively, they can be defined as matrices, all the hermitian quadratic forms of which are real and positive.
Wigner, Eugene P., Yanase, M. M.
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Linear Algebra and its Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qi, Houduo
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Applied Set-Valued Analysis and Optimization, 2023 We present an algorithm for computing the minimum-rank positive semidefinite completion of a sparse matrix with a chordal sparsity pattern. This problem is tractable, in contrast to the minimum-rank positive semidefinite completion problem for general sparsity patterns.
Jiang, Xin +3 more
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A Class of Weighted Low Rank Approximation of the Positive Semidefinite Hankel Matrix [PDF]
Journal of Applied Mathematics, 2015 We consider the weighted low rank approximation of the positive semidefinite Hankel matrix problem arising in signal processing. By using the Vandermonde representation, we firstly transform the problem into an unconstrained optimization problem and then
Jianchao Bai +3 more
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Binary positive semidefinite matrices and associated integer polytopes [PDF]
, 2012 We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes.We begin by establishing some basic properties of these matrices and polytopes.
Sorensen, M M, Letchford, A N
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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
Christian Mehl +2 more
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Uniqueness of size-2 positive semidefinite matrix factorizations
We characterize when a size-2 positive semidefinite (psd) factorization of a positive matrix of rank 3 and psd rank 2 is unique. The characterization is obtained using tools from rigidity theory. In the first step, we define s-infinitesimally rigid psd factorizations and characterize 1- and 2-infinitesimally rigid size-2 psd factorizations.
Dawson, Kristen +3 more
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Fast implementation for semidefinite programs with positive matrix completion [PDF]
Optimization Methods and Software, 2015 Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a sparse structure of input SDP by factorizing the variable matrices. In this paper, we propose a new factorization based on the inverse of the variable matrix
Makoto Yamashita, Kazuhide Nakata
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