Results 1 to 10 of about 6,368,085 (214)

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
doaj   +7 more sources

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
Volker Mehrmann, Michal Wojtylak
exaly   +4 more sources

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.
exaly   +4 more sources

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, Xuefeng Duan, Kexin Cheng, Xuewei Zhang   +3 more
doaj   +4 more sources

Polynomial Instances of the Positive Semidefinite and Euclidean Distance Matrix Completion Problems [PDF]

SIAM Journal on Matrix Analysis and Applications, 2001
Summary: Given an undirected graph \(G=(V,E)\) with node set \(V=[1,n]\), a set \(S\subseteq V\), and a rational vector \(a\in \mathbb{Q}^{S\cup E}\), the positive semidefinite matrix completion problem consists of determining whether there exists a real symmetric \(n\times n\) positive semidefinite matrix \(X=(x_{ij})\) satisfying \(x_{ii}= a_i\) \((i\
Monique Laurent
exaly   +4 more sources

Efficient Positive Semidefinite Matrix Approximation by Iterative Optimisations and Gradient Descent Method

Risks
We devise two algorithms for approximating solutions of PSDisation, a problem in actuarial science and finance, to find the nearest valid correlation matrix that is positive semidefinite (PSD).
Vali Asimit, Runshi Wang, Feng Zhou, Rui Zhu   +3 more
doaj   +3 more sources

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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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.
openaire   +4 more sources

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
doaj   +1 more source

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
openaire   +3 more sources