On the stability of gradient flow dynamics for a rank-one matrix approximation problem

2018 ◽  
Author(s):  
Hesameddin Mohammadi ◽  
Meisam Razaviyayn ◽  
Mihailo R. Jovanovic
Keyword(s):  
Gradient Flow ◽  
Approximation Problem ◽  
Flow Dynamics ◽  
Matrix Approximation ◽  
Rank One ◽  
The Stability

scholarly journals The core inverse and constrained matrix approximation problem

2020 ◽  
Vol 18 (1) ◽  
pp. 653-661 ◽  
Author(s):  
Hongxing Wang ◽  
Xiaoyan Zhang
Keyword(s):  
Unique Solution ◽  
Approximation Problem ◽  
Frobenius Norm ◽  
Matrix Approximation ◽  
The Core ◽  
Core Inverse

Abstract In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse: ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M), where M\in {{\mathbb{C}}}_{n}^{\text{CM}} . We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.

scholarly journals Geometric gradient-flow dynamics with singular solutions

2008 ◽  
Vol 237 (22) ◽  
pp. 2952-2965 ◽  
Author(s):  
Darryl D. Holm ◽  
Vakhtang Putkaradze ◽  
Cesare Tronci
Keyword(s):  
Gradient Flow ◽  
Flow Dynamics ◽  
Singular Solutions

Linear Stability Analysis in a Compressible Axisymmetric Swirling Jet

2014 ◽  
Vol 574 ◽  
pp. 15-20
Author(s):  
Zhi Wei Guo ◽  
Si Min Shen ◽  
Wei Min Feng ◽  
Bo Fu Wang
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Previous Analysis ◽  
Optimal Growth ◽  
Flow Dynamics ◽  
Swirl Number ◽  
Swirling Jet ◽  
Optimal Growth Rate ◽  
The Stability

Temporal linear stability of a compressible axisymmetric swirling jet is investigated. The present work extends a previous analysis to include the effects of swirl number on the stability of flow dynamics. Results obtained show that the optimal growth rate of disturbance for azimuthal wavenumber n = -1 is larger than that for n = -2 while the corresponding frequencies for both n increases as axial wavenumber increases. As swirl number q increases, the optimal growth rate of disturbance also increases. What is more, there is an optimal swirl number for small axial wavenumbers, which is different from the situation for medium and large axial wavenumbers.

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