A Positivity Preserving Inverse Iteration for Finding the Perron Pair of an Irreducible Nonnegative Third Order Tensor

2016 ◽  
Vol 37 (3) ◽  
pp. 911-932 ◽  
Author(s):  
Ching-Sung Liu ◽  
Chun-Hua Guo ◽  
Wen-Wei Lin
Keyword(s):  
Inverse Iteration ◽  
Third Order ◽  
Positivity Preserving ◽  
Order Tensor

A Novel Regularized Model for Third-Order Tensor Completion

2021 ◽  
pp. 1-1
Author(s):  
Yi Yang ◽  
Lixin Han ◽  
Yuanzhen Liu ◽  
Jun Zhu ◽  
Hong Yan
Keyword(s):  
Tensor Completion ◽  
Third Order ◽  
Order Tensor ◽  
Regularized Model

scholarly journals Robust Low-Tubal-Rank Tensor Completion via Convex Optimization

2019 ◽  
Author(s):  
Qiang Jiang ◽  
Michael Ng
Keyword(s):  
Degrees Of Freedom ◽  
L1 Norm ◽  
Third Order ◽  
Order Tensor ◽  
Rank Tensor ◽  
Real World Applications ◽  
Algebraic Framework ◽  
Tensor Nuclear Norm ◽  
Theoretical Results ◽  
Weighted Combination

This paper considers the problem of recovering multidimensional array, in particular third-order tensor, from a random subset of its arbitrarily corrupted entries. Our study is based on a recently proposed algebraic framework in which the tensor-SVD is introduced to capture the low-tubal-rank structure in tensor. We analyze the performance of a convex program, which minimizes a weighted combination of the tensor nuclear norm, a convex surrogate for the tensor tubal rank, and the tensor l1 norm. We prove that under certain incoherence conditions, this program can recover the tensor exactly with overwhelming probability, provided that its tubal rank is not too large and that the corruptions are reasonably sparse. The number of required observations is order optimal (up to a logarithm factor) when comparing with the degrees of freedom of the low-tubal-rank tensor. Numerical experiments verify our theoretical results and real-world applications demonstrate the effectiveness of our algorithm.

scholarly journals High-order tensor estimation via trains of coupled third-order CP and Tucker decompositions

2020 ◽  
Vol 588 ◽  
pp. 304-337 ◽  
Author(s):  
Yassine Zniyed ◽  
Rémy Boyer ◽  
André L.F. de Almeida ◽  
Gérard Favier
Keyword(s):  
High Order ◽  
Third Order ◽  
Order Tensor

scholarly journals Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion

2020 ◽  
Vol 29 ◽  
pp. 7233-7244
Author(s):  
Tai-Xiang Jiang ◽  
Michael K. Ng ◽  
Xi-Le Zhao ◽  
Ting-Zhu Huang
Keyword(s):  
Nuclear Norm ◽  
Tensor Completion ◽  
Third Order ◽  
Order Tensor ◽  
Tensor Nuclear Norm

scholarly journals Isotropic invariants of a completely symmetric third-order tensor

2014 ◽  
Vol 55 (9) ◽  
pp. 092901 ◽  
Author(s):  
M. Olive ◽  
N. Auffray
Keyword(s):  
Third Order ◽  
Order Tensor

High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates

2015 ◽  
Vol 25 (08) ◽  
pp. 1553-1588 ◽  
Author(s):  
Yan Jiang ◽  
Chi-Wang Shu ◽  
Mengping Zhang
Keyword(s):  
Random Walk ◽  
Finite Difference ◽  
Temporal Integration ◽  
Time Discretization ◽  
High Order ◽  
Correlated Random Walk ◽  
Third Order ◽  
Positivity Preserving ◽  
Fifth Order ◽  
High Order Finite Difference

In this paper, we discuss high-order finite difference weighted essentially non-oscillatory schemes, coupled with total variation diminishing (TVD) Runge–Kutta (RK) temporal integration, for solving the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology. Since the solutions to this system are non-negative, we discuss a positivity-preserving limiter without compromising accuracy. Analysis is performed to justify the maintenance of third-order spatial/temporal accuracy when the limiters are applied to a third-order finite difference scheme and third-order TVD-RK time discretization for solving this model. Numerical results are also provided to demonstrate these methods up to fifth-order accuracy.

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