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Exact barycentric rational interpolation of analytic functions with an application to the Bessel functions

  • Brett R. Green
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Abstract

We derive a method of analytic function expansion using barycentric rational interpolation, in which an arbitrary analytic weight function defines the interpolation and nodes. Truncating these expansions yields successive approximations, and the derivation of the expansions gives the approximation error as a byproduct. We demonstrate the method with cosine and the Bessel functions of the first kind for several choices of weight functions, and we examine the accuracy and convergence of the approximate interpolations as a function of the weight and the number of nodes used in the interpolation.

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Cite

BibTeXRIS
BibTeX
@misc{green2026exact,
  title = {{Exact barycentric rational interpolation of analytic functions with an application to the Bessel functions}},
  author = {Brett R. Green},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39805},
  eprint = {2609.39805},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39805},
}
RIS
TY  - UNPB
TI  - Exact barycentric rational interpolation of analytic functions with an application to the Bessel functions
AU  - Brett R. Green
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39805
UR  - https://arxiv.org/abs/2609.39805
AB  - We derive a method of analytic function expansion using barycentric rational interpolation, in which an arbitrary analytic weight function defines the interpolation and nodes. Truncating these expansions yields successive approximations, and the derivation of the expansions gives the approximation error as a byproduct. We demonstrate the method with cosine and the Bessel functions of the first kind for several choices of weight functions, and we examine the accuracy and convergence of the approximate interpolations as a function of the weight and the number of nodes used in the interpolation.
ER  -