34 citations · 63 across the 16 of their papers we have counts for
6 papers · 1 filter
On the backward stability of the second barycentric formula for interpolation
Walter F. Mascarenhas, Andre Pierro de Camargo
We present a new stability analysis for the second barycentric formula for interpolation, showing that this formula is backward stable when the relevant Lebesgue constant is small.
The divergence of the barycentric Pade approximants
Walter F. Mascarenhas
We explain that, like the usual Padé approximants, the barycentric Padé approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More precisely, we show that for…
The divergence of the BFGS and Gauss Newton Methods
Walter F. Mascarenhas
We present examples of divergence for the BFGS and Gauss Newton methods. These examples have objective functions with bounded level sets and other properties concerning the example…
The effects of rounding errors in the nodes on barycentric interpolation
Walter F. Mascarenhas, André Pierro de Camargo
We analyze the effects of rounding errors in the nodes on barycentric interpolation. These errors are particularly relevant for the first barycentric formula with the Chebyshev poi…
The stability of barycentric interpolation at the Chebyshev points of the second kind
Walter F. Mascarenhas
We present a new analysis of the stability of the first and second barycentric formulae for interpolation at the Chebyshev points of the second kind. Our theory shows that the seco…
Robust Pade approximants may have spurious poles
Walter F. Mascarenhas
We show that robust Pade approximants may have spurious poles and may not converge pointwise