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On the robustness of exponential base terms and the Padé denominator in some least squares sense

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Abstract

The exponential analysis of 2n uniformly collected samples from an n-term exponential sum is equivalent to the reconstruction of a rational function of degree n −1 over n. The latter is by computing the Padé approximant of the z-transform of the sequence of samples. In practice, the samples are often noisy and 2n is replaced by N > 2ν with ν > n, leading to a least squares computation of the Padé approximant of degree ν −1 over ν. We show that the latter is a perturbed version of the one of degree n −1 over n and that the n exponential base terms can still be retrieved reliably. This has remained an open problem for many years, despite the fact that the least squares computation was used in most applications.

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Funding

This research has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101008231 (EXPOWER).

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Authors and Affiliations

  1. Department of Computer Science, Universiteit Antwerpen, Middelheimlaan 1, Antwerpen, Belgium

    Ferre Knaepkens & Annie Cuyt

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  1. Ferre Knaepkens
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  2. Annie Cuyt
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Correspondence to Ferre Knaepkens.

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The datasets generated during this study are available on the CEMath webpage at https://cemath.org/publications/papers/.

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To the 80th birthday of Claude Brezinski, our very respected colleague in Padé approximation research.

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Knaepkens, F., Cuyt, A. On the robustness of exponential base terms and the Padé denominator in some least squares sense. Numer Algor 92, 747–766 (2023). https://doi.org/10.1007/s11075-022-01455-z

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  • DOI: https://doi.org/10.1007/s11075-022-01455-z

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