Stefano De Marchi (Università di Padova): On "fake" nodes for polynomial approximation

In this talk we propose a new method for polynomial interpolation  based on *mapped bases*. As theoretically shown, constructing the  interpolating function via the mapped bases, turns out to be  equivalent to map the nodes and then construct the approximant in the  classical form without the need of resampling. In view of this, we  also refer to such mapped points as "fake nodes". We present a general  algorithm for constructing the mapping function.
We also discuss some examples to confirm that such scheme can be  applied to substantially reduce both the Runge and Gibbs phenomena in  univariate setting and in imaging.

Joint work with F. Marchetti, E. Perracchione and D. Poggiali  (University of Padova)