Sun Mar 31 16:18:59 EDT 2013

Iteration and polynomial interpolation

Thinking about recent ad--hoc experiments with polynomial iteration.
However, there is a classical poly approx method that does successive
refinement, adding one approximation point at a time.  This would be
Newton interpolation.  It's not really what I had in mind though..
Overview from "Inleiding tot de numerieke wiskunde" - Adhemar

- Linear equation - Vandermonde matrix

- Lagange: sum of base polynomials  f_n at x=x_n and 0 at x=x_i, i!=n

- Newton: successive approximation, one data point per step +
  specialization for equidistant, ...

- Hermite: also derivatives