Continuation methods for nonnegative rank‐1 approximation of nonnegative tensors

2021 ◽  
Author(s):  
Fu‐Shin Hsu ◽  
Yueh‐Cheng Kuo ◽  
Ching‐Sung Liu
Keyword(s):  
Continuation Methods ◽  
Nonnegative Tensors ◽  
Nonnegative Rank

scholarly journals Continuation methods for computing Z-/H-eigenpairs of nonnegative tensors

2018 ◽  
Vol 340 ◽  
pp. 71-88 ◽  
Author(s):  
Yueh-Cheng Kuo ◽  
Wen-Wei Lin ◽  
Ching-Sung Liu
Keyword(s):  
Continuation Methods ◽  
Nonnegative Tensors

scholarly journals Some inequalities on the spectral radius of nonnegative tensors

2020 ◽  
Vol 18 (1) ◽  
pp. 262-269
Author(s):  
Chao Ma ◽  
Hao Liang ◽  
Qimiao Xie ◽  
Pengcheng Wang
Keyword(s):  
Spectral Radius ◽  
Nonnegative Tensors

Abstract The eigenvalues and the spectral radius of nonnegative tensors have been extensively studied in recent years. In this paper, we investigate the analytic properties of nonnegative tensors and give some inequalities on the spectral radius.

Solution Fields of Nonlinear Equations and Continuation Methods

1980 ◽  
Vol 17 (2) ◽  
pp. 221-237 ◽  
Author(s):  
Werner C. Rheinboldt
Keyword(s):  
Nonlinear Equations ◽  
Continuation Methods

Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations

SIAM Review ◽  
1980 ◽  
Vol 22 (1) ◽  
pp. 28-85 ◽  
Author(s):  
Eugene Allgower ◽  
Kurt Georg
Keyword(s):  
Fixed Points ◽  
Continuation Methods ◽  
Systems Of Equations

Approximate Nonnegative Rank is Equivalent to the Smooth Rectangle Bound

2018 ◽  
Vol 28 (1) ◽  
pp. 1-25
Author(s):  
Gillat Kol ◽  
Shay Moran ◽  
Amir Shpilka ◽  
Amir Yehudayoff
Keyword(s):  
Nonnegative Rank

Continuation Methods in Boundary Value Problems

1994 ◽  
pp. 65-70 ◽  
Author(s):  
Vassili V. Dikoussar
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Continuation Methods

scholarly journals Stationary localized structures and the effect of the delayed feedback in the Brusselator model

2018 ◽  
Vol 376 (2135) ◽  
pp. 20170385 ◽  
Author(s):  
B. Kostet ◽  
M. Tlidi ◽  
F. Tabbert ◽  
T. Frohoff-Hülsmann ◽  
S. V. Gurevich ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Dissipative Structures ◽  
Delayed Feedback ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Delayed Feedback Control ◽  
Brusselator Model ◽  
Localized Structures ◽  
Reaction Diffusion Model ◽  
Spatial Dimensions

The Brusselator reaction–diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator model. By using numerical continuation methods in two spatial dimensions, we establish a bifurcation diagram showing the emergence of localized spots. We characterize the transition from a single spot to an extended pattern in the form of squares. In the second part, we incorporate delayed feedback control and show that delayed feedback can induce a spontaneous motion of both localized and periodic dissipative structures. We characterize this motion by estimating the threshold and the velocity of the moving dissipative structures. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

scholarly journals Fast Decomposition of Large Nonnegative Tensors

2015 ◽  
Vol 22 (7) ◽  
pp. 862-866 ◽  
Author(s):  
Jeremy E. Cohen ◽  
Rodrigo Cabral Farias ◽  
Pierre Comon
Keyword(s):  
Nonnegative Tensors ◽  
Fast Decomposition

Nonnegative rank factorization—a heuristic approach via rank reduction

2013 ◽  
Vol 65 (2) ◽  
pp. 251-274 ◽  
Author(s):  
Bo Dong ◽  
Matthew M. Lin ◽  
Moody T. Chu
Keyword(s):  
Heuristic Approach ◽  
Rank Reduction ◽  
Nonnegative Rank ◽  
Rank Factorization
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