Lecture 20.
Interpolation demos.
Today I we saw some illuminating
demonstrations, using Matlab, pertaining to polynomial interpolation.
We started with an exploration of
full degree polynomial interpolation and the demonstration programs from
Recktenwald:
demoGasNewt, demoGasLag,
and demoGasVand. The main observation is that the poor scaling of the
Vandermonde matrix yields visual artifacts in the polynomial plot.
At this point we returned to
root finding and the hybrid algorithm that uses Inverse Quadratic Interpolation
IQI. We use the fzerogui program from Moler to explore this algorithm.
Tomorrow I will be deriving
formulae for piece-wise interpolation. I used the interpgui program also from
Moler to provide some visual intuition for upcoming lectures.
Posted: Thu - October 27, 2005 at 12:05 PM