  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 current literature, we show that the
Lebesgue constant of these interpolants can grow exponentially with the
parameters that define them, and we emphasize the importance of using the
proper interpretation of the Lebesgue constant in order to estimate correctly
the effects of noise and rounding errors. We also present a simple condition
that implies the backward instability of the barycentric formula used to
implement extended interpolants. Our experiments show that extended
interpolants mentioned in the literature satisfy this condition and, therefore,
the formula used to implement them is not backward stable. Finally, we explain
that the extrapolation step is a significant source of numerical instability
for extended interpolants based on extrapolation.
