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