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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
Bultheel.
- 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

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