Newton correction methods for computing real eigenpairs of symmetric tensors

Ariel Jaffe, Roi Weiss, Boaz Nadler

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions for a real eigenpair to be a stable fixed point for our method and prove that given a sufficiently close initial guess, the convergence rate is quadratic. Empirically, our method converges to a significantly larger number of eigenpairs compared with previously proposed iterative methods, and with enough random initializations typically finds all real eigenpairs. In particular, for a generic symmetric tensor, the sufficient conditions for local convergence of our Newton-based method hold simultaneously for all its real eigenpairs.

Original languageAmerican English
Pages (from-to)1071-1094
Number of pages24
JournalSIAM Journal on Matrix Analysis and Applications
Volume39
Issue number3
DOIs
StatePublished - 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.

Keywords

  • Higher-order power method
  • Newton correction method
  • Newton-based methods
  • Symmetric tensor
  • Tensor eigenvalues
  • Tensor eigenvectors

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