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- W3025254620 abstract "A crucial question in large non-Hermitian eigenproblems is whether or not any residual bounds can be very useful in practical situations. For this problem, the famous Kahan-Parlett-Jiang theorem Kahan et al. (1982) [15] seems to be the best compromise between generality and sharpness. In essence, it presents an a posteriori error bound on approximate solutions to eigenproblems, which provides a powerful tool to evaluate quality of the computed two-sided invariant subspaces of large-scale non-Hermitian matrices. However, the perturbation error determined by this theorem is only locally optimal rather than globally optimal. In this work, we revisit this problem and derive a globally optimal backward perturbation error for given two-sided approximate invariant subspaces. Our theorem enhances the Kahan-Parlett-Jiang theorem, and numerical experiments demonstrate the effectiveness of our theoretical results." @default.
- W3025254620 created "2020-05-21" @default.
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- W3025254620 date "2020-10-01" @default.
- W3025254620 modified "2023-09-25" @default.
- W3025254620 title "On the Kahan-Parlett-Jiang theorem—A globally optimal backward perturbation error for two-sided invariant subspaces" @default.
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- W3025254620 doi "https://doi.org/10.1016/j.laa.2020.05.003" @default.
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