A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map

Qin Ni, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)

Abstract

In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map where the Newton method is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between homogeneous polynomial map and its associated semi-symmetric tensor. Based on this relation a globally and quadratically convergent algorithm is established where the line search is inserted. Some numerical results of this method are reported.
Original languageEnglish
Pages (from-to)627-641
Number of pages15
JournalJournal of Global Optimization
Volume61
Issue number4
DOIs
Publication statusPublished - 22 Mar 2015

Keywords

  • Eigenvalue of polynomial mapping
  • Newton method
  • Nonnegative homogenous polynomial mapping
  • Nonnegative tensors

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this