Abstract
We show that a multiple eigenvalue has different sensitivities under perturbations in a generalized Hermitian eigenvalue problem. Our result provides a solution to a question raised by Stewart and Sun. We also show how this difference of sensitivities plays a role in the eigenvalue forward error analysis after the Rayleigh-Ritz process, for which we present an approach that provides tight bounds.
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Communicated by Axel Ruhe.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nakatsukasa, Y. Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems. Bit Numer Math 50, 109–121 (2010). https://doi.org/10.1007/s10543-010-0254-8
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DOI: https://doi.org/10.1007/s10543-010-0254-8