On the conditioning of some structured generalized eigenvalue problems

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...

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Bibliographic Details
Published inMaple Transactions Vol. 3; no. 3
Main Authors Cuyt, Annie, Flamand, Naomi, Knaepkens, Ferre
Format Journal Article
LanguageEnglish
Published 02.11.2023
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Summary: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.
ISSN:2564-3029
2564-3029
DOI:10.5206/mt.v3i3.16450