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arXiv · 1906.09942

Pole-swapping algorithms for alternating and palindromic eigenvalue problems

Thomas Mach·Thijs Steel·Raf Vandebril·David S. Watkins
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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.

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Thomas Mach, Thijs Steel, Raf Vandebril, David S. Watkins. 2019-12-09. Pole-swapping algorithms for alternating and palindromic eigenvalue problems. https://arxiv.org/abs/1906.09942

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