On the conditioning of some structured generalized eigenvalue problems
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Bibliographic record
Abstract
This work continues the analysis of the conditioning of a Hankel structured generalized eigenvalue problem (GEP) started in [1]. The considered generalized eigenvalue problem appears in exponential analysis and sparse interpolation. We generalize the proof in [1] and add expressions for the relative condition numbers of two reformulations of the GEP, a reformulation as a Loewner GEP valid for general complex data, and a compression to a Hankel+Toeplitz GEP in the case of real data. Both reformulations are compared to the original Hankel GEP. The analysis is concluded with ample numerical illustrations.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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