Tensor decomposition and homotopy continuation

Dataset

Description

A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness sets via numerical elimination theory, we develop computational methods for computing ranks and border ranks of tensors along with decompositions. More generally, we present our approach using joins of any collection of irreducible and nondegenerate projective varieties X1,..,Xk contained in P^N defined over C. After computing ranks over C, we also explore computing real ranks. A variety of examples are included to demonstrate the numerical algebraic geometric approaches.

Attributes

Attribute NameValues
Creator
  • Jonathan Hauenstein

Contributor
  • Alessandra Bernardi

  • Noah Daleo

  • Bernard Mourrain

Publisher
  • Jonathan Hauenstein

Departments and Units
Record Visibility and Access Public
Content License
  • All rights reserved

Digital Object Identifier

doi:10.7274/R0DR2SDZ

This DOI is the best way to cite this dataset.


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