We present three new developments in rational interpolation.
First we discuss the near optimal placement of interpolation points for
a given (but arbitrary) set of poles. Then we study rational
interpolation in the presence of measurement errors (approximation of
vertical segments). In the last part we present a fast and stable
algorithm for rational interpolation in Chebyshev points. Several
examples and applications illustrate these theoretical developments.
[Invited by Prof. Jean-Paul Berrut]