Tensor Bi-CR Methods for Solutions of High Order Tensor Equation Accompanied by Einstein Product

2021 ◽  
Vol 14 (4) ◽  
pp. 998-1016
Author(s):  
Masoud Hajarian
Keyword(s):  
High Order ◽  
Tensor Equation ◽  
Order Tensor ◽  
Einstein Product

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 Iterative solution of quadratic tensor equations for mutual polarisation

2002 ◽  
Vol 32 (5) ◽  
pp. 301-312 ◽  
Author(s):  
Wynand S. Verwoerd
Keyword(s):  
Dipole Moment ◽  
Linear Approximation ◽  
Iterative Solution ◽  
Second Order ◽  
Local Fields ◽  
Bulk Materials ◽  
Tensor Equation ◽  
Order Tensor ◽  
Intrinsic Values ◽  
Induced Dipole

To describe mutual polarisation in bulk materials containing high polarisability molecules, local fields beyond the linear approximation need to be included. A second order tensor equation is formulated, and it describes this in the case of crystalline or at least locally ordered materials such as an idealised polymer. It is shown that this equation is solved by a set of recursion equations that relate the induced dipole moment, linear polarisability, and first hyperpolarisability in the material to the intrinsic values of the same properties of isolated molecules. From these, macroscopic susceptibility tensors up to second order can be calculated for the material.

Low-Complexity Multidimensional DCT Approximations for High-Order Tensor Data Decorrelation

2017 ◽  
Vol 26 (5) ◽  
pp. 2296-2310 ◽  
Author(s):  
Vitor A. de A. Coutinho ◽  
Renato J. Cintra ◽  
Fabio M. Bayer
Keyword(s):  
Low Complexity ◽  
High Order ◽  
Order Tensor ◽  
Tensor Data
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