scholarly journals A New Algorithm for Positive Semidefinite Matrix Completion

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Fangfang Xu ◽  
Peng Pan
Keyword(s):  
Matrix Completion ◽  
Positive Semidefinite ◽  
Alternating Direction Method ◽  
Low Rank ◽  
System Control ◽  
Positive Semidefinite Matrix ◽  
Linear Least Squares ◽  
Alternating Direction ◽  
Semidefinite Matrix Completion ◽  
Semidefinite Matrix

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. This task can be conducted by solving the nuclear norm regularized linear least squares model with positive semidefinite constraints. We apply the widely used alternating direction method of multipliers to solve the model and get a novel algorithm. The applicability and efficiency of the new algorithm are demonstrated in numerical experiments. Recovery results show that our algorithm is helpful.

scholarly journals Millimeter-Wave Channel Estimation using Alternating Direction Method of Multipliers

2021 ◽  
Vol 10 (4) ◽  
pp. 239-242
Author(s):  
Aarab Mohamed Nassim ◽  
Chakkor Otman
Keyword(s):  
Channel Estimation ◽  
Millimeter Wave ◽  
Mobile Networks ◽  
Mimo Systems ◽  
Matrix Completion ◽  
Mobile Network ◽  
Alternating Direction Method ◽  
Low Rank ◽  
Wave Channel ◽  
Alternating Direction

With the explosive growth in demand for mobile data traffic, the contradiction between capacity requirements and spectrum scarcity becomes more and more prominent. The bandwidth is becoming a key issue in 5G mobile networks. However, with the huge bandwidth from 30 GHz to 300 GHz, mmWave communications considered an important part of the 5G mobile network providing multi communication services, where channel state information considers a challenging task for millimeter wave MIMO systems due to the huge number of antennas. Therefore, this paper discusses the channel and signal models of the mmWave, with a novel formulation for mmWave channel estimation inclusive low rank features, that we improved using a developed theory of matrix completion with Alternating Direction Method.

scholarly journals Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Minghua Xu ◽  
Yong Zhang ◽  
Qinglong Huang ◽  
Zhenhua Yang
Keyword(s):  
Optimization Problems ◽  
Positive Semidefinite ◽  
Numerical Linear Algebra ◽  
Alternating Direction Method ◽  
Matrix Optimization ◽  
Finance Industry ◽  
Alternating Direction ◽  
Closed Convex Set ◽  
Semidefinite Matrix ◽  
Proximal Alternating Direction Method

We consider the problem of seeking a symmetric positive semidefinite matrix in a closed convex set to approximate a given matrix. This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. For solving this class of matrix optimization problems, many methods have been proposed in the literature. The proximal alternating direction method is one of those methods which can be easily applied to solve these matrix optimization problems. Generally, the proximal parameters of the proximal alternating direction method are greater than zero. In this paper, we conclude that the restriction on the proximal parameters can be relaxed for solving this kind of matrix optimization problems. Numerical experiments also show that the proximal alternating direction method with the relaxed proximal parameters is convergent and generally has a better performance than the classical proximal alternating direction method.

scholarly journals A trace bound for integer-diagonal positive semidefinite matrices

2020 ◽  
Vol 8 (1) ◽  
pp. 14-16
Author(s):  
Lon Mitchell
Keyword(s):  
Positive Semidefinite ◽  
Positive Semidefinite Matrix ◽  
Positive Semidefinite Matrices ◽  
Semidefinite Matrix

AbstractWe 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.

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