34 citations · 63 across the 16 of their papers we have counts for
10 papers · 1 filter
Root Finding With Interval Arithmetic
Walter F. Mascarenhas
We consider the solution of nonlinear equations in one real variable, the problem usually called by root finding. Although this is an old problem, we believe that some aspects of i…
On the rate of convergence of Berrut's interpolant at equally spaced nodes
Walter F. Mascarenhas
We extend the work by Mastroianni and Szabados regarding the barycentric interpolant introduced by J.-P. Berrut in 1988, for equally spaced nodes. We prove fully their first conjec…
Floating point numbers are real numbers
Walter F. Mascarenhas
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the…
A rational Rodrigues' formula to interpolate rotations
Walter F. Mascarenhas
We propose a rational version of the classic Rodrigues' rotation formula, which leads to a more accurate and efficient modelling of rotations and their derivatives in finite precis…
The stability of extended Floater-Hormann interpolants
Andre Pierro de Camargo, Walter F. Mascarenhas
We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the…
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 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