English

The divergence of the barycentric Pade approximants

Numerical Analysis 2014-08-15 v3

Abstract

We explain that, like the usual Pad\'e approximants, the barycentric Pad\'e approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More precisely, we show that for every polynomial P there exists a power series S, with arbitrarily small coefficients, such that the sequence of barycentric Pad\'e approximants of P + S do not converge uniformly in any subset of the complex plane with a non-empty interior.

Keywords

Cite

@article{arxiv.1310.1045,
  title  = {The divergence of the barycentric Pade approximants},
  author = {Walter F. Mascarenhas},
  journal= {arXiv preprint arXiv:1310.1045},
  year   = {2014}
}

Comments

Introducted a new section describing informally the proof of the main theorem