Generating Polynomials and Symmetric Tensor Decompositions
Sign Up to like & getrecommendations! Published in 2017 at "Foundations of Computational Mathematics"
DOI: 10.1007/s10208-015-9291-7
Abstract: This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial. The… read more here.
Keywords: tensor decompositions; matrix; tensor; symmetric tensor ... See more keywords
The product of the eigenvalues of a symmetric tensor
Sign Up to like & getrecommendations! Published in 2018 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2018.05.033
Abstract: Abstract We study E-eigenvalues of a symmetric tensor f of degree d on a finite-dimensional Euclidean vector space V, and their relation with the E-characteristic polynomial of f. We show that the leading coefficient of… read more here.
Keywords: eigenvalues symmetric; product; characteristic polynomial; symmetric tensor ... See more keywords
Riemannian Newton optimization methods for the symmetric tensor approximation problem
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DOI: 10.1016/j.laa.2021.12.008
Abstract: The Symmetric Tensor Approximation problem (STA) consists of approximating a symmetric tensor or a homogeneous polynomial by a linear combination of symmetric rank-1 tensors or powers of linear forms of low symmetric rank. We present… read more here.
Keywords: newton; tensor; symmetric tensor; approximation problem ... See more keywords
How many eigenvalues of a random symmetric tensor are real?
Sign Up to like & getrecommendations! Published in 2019 at "Transactions of the American Mathematical Society"
DOI: 10.1090/tran/7910
Abstract: This article answers a question posed by Draisma and Horobet, who asked for a closed formula for the expected number of real eigenvalues of a random real symmetric tensor drawn from the Gaussian distribution relative… read more here.
Keywords: symmetric tensor; random symmetric; many eigenvalues; tensor real ... See more keywords
Robust and Fast Extraction of 3D Symmetric Tensor Field Topology
Sign Up to like & getrecommendations! Published in 2019 at "IEEE Transactions on Visualization and Computer Graphics"
DOI: 10.1109/tvcg.2018.2864768
Abstract: 3D symmetric tensor fields appear in many science and engineering fields, and topology-driven analysis is important in many of these application domains, such as solid mechanics and fluid dynamics. Degenerate curves and neutral surfaces are… read more here.
Keywords: tensor; symmetric tensor; neutral surfaces; topology ... See more keywords
Complementation in the Fremlin vector lattice symmetric tensor products-I
Sign Up to like & getrecommendations! Published in 2019 at "Quaestiones Mathematicae"
DOI: 10.2989/16073606.2019.1605422
Abstract: Abstract For a positive integer n and a uniformly complete vector lattice E, let denote the n-fold Fremlin vector lattice symmetric tensor product of E. We prove that if there exists a lattice homomorphism φ… read more here.
Keywords: lattice symmetric; fremlin vector; symmetric tensor; vector lattice ... See more keywords
Spacetimes admitting the Z-symmetric tensor
Sign Up to like & getrecommendations! Published in 2020 at "Quaestiones Mathematicae"
DOI: 10.2989/16073606.2020.1816587
Abstract: This paper aims to introduce the spacetimes admitting the Z-symmetric tensor. We investigate the properties of these spacetimes for a perfect fluid and a pressureless perfect fluid (a dust). Some theorems about the properties are… read more here.
Keywords: admitting symmetric; symmetric tensor; spacetimes admitting;