English

Pole-swapping algorithms for alternating and palindromic eigenvalue problems

Numerical Analysis 2019-12-11 v2 Numerical Analysis

Abstract

Pole-swapping algorithms are generalizations of bulge-chasing algorithms for the generalized eigenvalue problem. Structure-preserving pole-swapping algorithms for the palindromic and alternating eigenvalue problems, which arise in control theory, are derived. A refinement step that guarantees backward stability of the algorithms is included. This refinement can also be applied to bulge-chasing algorithms that had been introduced previously, thereby guaranteeing their backward stability in all cases.

Keywords

Cite

@article{arxiv.1906.09942,
  title  = {Pole-swapping algorithms for alternating and palindromic eigenvalue problems},
  author = {Thomas Mach and Thijs Steel and Raf Vandebril and David S. Watkins},
  journal= {arXiv preprint arXiv:1906.09942},
  year   = {2019}
}
R2 v1 2026-06-23T10:01:55.258Z