On the complexity of isomorphism problems for tensors, groups, and polynomials III: actions by classical groups

Z Chen, JA Grochow, Y Qiao, G Tang… - arxiv preprint arxiv …, 2023 - arxiv.org
We study the complexity of isomorphism problems for d-way arrays, or tensors, under natural
actions by classical groups such as orthogonal, unitary, and symplectic groups. Such …

[PDF][PDF] Tree tensor networks, associated singular values and high-dimensional approximation

S Krämer - 2020 - publications.rwth-aachen.de
In this thesis, we develop an algebraic and graph theoretical reinterpretation of tensor
networks and formats. We investigate properties of associated singular values and …

[Књига][B] Structured tensors and the geometry of data

AL Seigal - 2019 - search.proquest.com
We analyze data to build a quantitative understanding of the world. Linear algebra is the
foundation to algorithms, dating back one hundred years, for extracting structure from data …

A geometric description of feasible singular values in the tensor train format

S Krämer - SIAM Journal on Matrix Analysis and Applications, 2019 - SIAM
Tree tensor networks such as the tensor train (TT) format are a common tool for high-
dimensional problems. The associated multivariate rank and accordant tuples of singular …

Completely positive binary tensors

J Fan, J Nie, A Zhou - Mathematics of Operations Research, 2019 - pubsonline.informs.org
A symmetric tensor is completely positive (CP) if it is a sum of tensor powers of nonnegative
vectors. This paper characterizes completely positive binary tensors. We show that a binary …

On the largest multilinear singular values of higher-order tensors

I Domanov, A Stegeman, LD Lathauwer - SIAM Journal on Matrix Analysis and …, 2017 - SIAM
Let \sigma_n denote the largest mode-n multilinear singular value of an I_1*\dots*I_N tensor
\mathcalT. We prove that \sigma_1^2+\dots+n-1^2+n+1^2+\dots+N^2≦(N …

Leibniz International Proceedings in Informatics (LIPIcs): 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Z Chen, JA Grochow, Y Qiao, G Tang, C Zhang - 2024 - par.nsf.gov
We study the complexity of isomorphism problems for d-way arrays, or tensors, under natural
actions by classical groups such as orthogonal, unitary, and symplectic groups. These …