Pole-swapping algorithms for alternating and palindromic eigenvalue problems
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.09942
- arXiv:
- arXiv:1906.09942
- Bibcode:
- 2019arXiv190609942M
- Keywords:
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- Mathematics - Numerical Analysis