Walter F. Mascarenhas
Published 2013-10-03, updated 2014-08-14Version 3
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.
Comments: Introducted a new section describing informally the proof of the main theorem
Accuracy and stability of inversion of power series
Evaluation of Abramowitz functions in the right half of the complex plane
Stability analyses of divergence and vorticity damping on gnomonic cubed-sphere grids
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