FakeNodes

Python code for Fake Nodes interpolation approach.

Fake nodes approach gives the possibility to obtain a better interpolation without getting new samples!

For the implementation of the fake nodes approach in 2D we refer to https://github.com/pog87/FakeNodes2D

Quote this work

To use this work in any scientific report or publication, please cite:

• S. De Marchi, F. Marchetti, E. Perracchione, D. Poggiali, Polynomial interpolation via mapped bases without resampling link, JCAM.

What are Fake Nodes

Fake Nodes is a novel approach to numerical interpolation that aims to achieve a better interpolation without having to get new samples. You can use your samples as they were taken at better/more representative nodes, cheating with the interpolation domain by applying a map.

In terms of code: suppose you have an interpolation function

def my_fancy_interpolator(x,y,xx):
  .......
  .......
  return yy

and a mapping S = lambda x: ...., if you want to use the fake nodes interpolation it is sufficient to call

yy = my_fancy_interpolator(S(x),y,S(xx))

...very simple, isn't it? Yet the theory standing behind this scheme is not that trivial..check it out!.

In the next notebooks, we will show the treatment of two classical phenomena in polynomial interpolation: the Runge effect and the Gibbs effect.