Perturbation bounds of tensor eigenvalue and singular value problems with even order

Maolin Che, Liqun Qi, Yimin Wei

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

The main purpose of this paper is to investigate the perturbation bounds of the tensor eigenvalue and singular value problems with even order. We extend classical definitions from matrices to tensors, such as, (Formula presented.) -tensor and the tensor polynomial eigenvalue problem. We design a method for obtaining a mode-symmetric embedding from a general tensor. For a given tensor, if the tensor is mode-symmetric, then we derive perturbation bounds on an algebraic simple eigenvalue and Z-eigenvalue. Otherwise, based on symmetric or mode-symmetric embedding, perturbation bounds of an algebraic simple singular value are presented. For a given tensor tuple, if all tensors in this tuple are mode-symmetric, based on the definition of a (Formula presented.) -tensor, we estimate perturbation bounds of an algebraic simple polynomial eigenvalue. In particular, we focus on tensor generalized eigenvalue problems and tensor quadratic eigenvalue problems.
Original languageEnglish
Pages (from-to)622-652
Number of pages31
JournalLinear and Multilinear Algebra
Volume64
Issue number4
DOIs
Publication statusPublished - 2 Apr 2016

Keywords

  • algebraic simple
  • mode-k tensor polynomial eigenvalue
  • mode-symmetric embedding
  • mode-symmetry
  • nonsingular tensor
  • tensor generalized eigenvalue
  • tensor generalized singular value
  • tensor quadratic eigenvalue

ASJC Scopus subject areas

  • Algebra and Number Theory

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