scholarly journals Systems of Polynomial Equations, Higher-Order Tensor Decompositions, and Multidimensional Harmonic Retrieval: A Unifying Framework. Part II: The Block Term Decomposition

2021 ◽  
Vol 42 (2) ◽  
pp. 913-953
Author(s):  
Jeroen Vanderstukken ◽  
Patrick Kürschner ◽  
Ignat Domanov ◽  
Lieven De Lathauwer
Keyword(s):  
Higher Order ◽  
Polynomial Equations ◽  
Order Tensor ◽  
Tensor Decompositions ◽  
Harmonic Retrieval ◽  
Multidimensional Harmonic Retrieval ◽  
Systems Of Polynomial Equations ◽  
Block Term Decomposition

scholarly journals Blind fMRI source unmixing via higher-order tensor decompositions

2019 ◽  
Vol 315 ◽  
pp. 17-47 ◽  
Author(s):  
Christos Chatzichristos ◽  
Eleftherios Kofidis ◽  
Manuel Morante ◽  
Sergios Theodoridis
Keyword(s):  
Higher Order ◽  
Order Tensor ◽  
Tensor Decompositions

Construction of systems of polynomial equations with exact p-Divisibility via the covering method

2014 ◽  
Vol 13 (06) ◽  
pp. 1450013 ◽  
Author(s):  
Francis N. Castro ◽  
Ivelisse M. Rubio
Keyword(s):  
Exponential Sums ◽  
Polynomial Equations ◽  
Prime Field ◽  
Elementary Method ◽  
Covering Method ◽  
Systems Of Polynomial Equations

We present an elementary method to compute the exact p-divisibility of exponential sums of systems of polynomial equations over the prime field. Our results extend results by Carlitz and provide concrete and simple conditions to construct families of polynomial equations that are solvable over the prime field.

Assessing the Use of Tensor Closure Methods With Orientation Distribution Reconstruction Functions

Materials ◽  
2003 ◽  
Author(s):  
David A. Jack ◽  
Douglas E. Smith
Keyword(s):  
Distribution Function ◽  
Fourth Order ◽  
Lower Order ◽  
Series Representation ◽  
Orientation Distribution ◽  
Higher Order ◽  
Interaction Coefficients ◽  
Order Tensor ◽  
Orientation Tensor ◽  
Orientation Tensors

Orientation tensors are widely used to describe fiber distri-butions in short fiber reinforced composite systems. Although these tensors capture the stochastic nature of concentrated fiber suspensions in a compact form, the evolution equation for each lower order tensor is a function of the next higher order tensor. Flow calculations typically employ a closure that approximates the fourth-order orientation tensor as a function of the second order orientation tensor. Recent work has been done with eigen-value based and invariant based closure approximations of the fourth-order tensor. The effect of using lower order tensors tensors in process simulations by reconstructing the distribution function from successively higher order orientation tensors in a Fourier series representation is considered. This analysis uses the property that orientation tensors are related to the series expansion coefficients of the distribution function. Errors for several closures are investigated and compared with errors developed when using a reconstruction from the exact 2nd, 4th, and 6th order orientation tensors over a range of interaction coefficients from 10−4 to 10−1 for several flow fields.

scholarly journals Linear Network Codes and Systems of Polynomial Equations

2008 ◽  
Vol 54 (5) ◽  
pp. 2303-2316 ◽  
Author(s):  
Randall Dougherty ◽  
Chris Freiling ◽  
Kenneth Zeger
Keyword(s):  
Polynomial Equations ◽  
Linear Network ◽  
Network Codes ◽  
Systems Of Polynomial Equations
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