I have a set of estimated points, listed below, and I would like to know how to calculate the polynomial.
I've looked at Wikipedia, and I don't quite understand how at works. Example 1 on http://en.wikipedia.org/wiki/Lagrange_polynomial#Example_1 seems to be the closest to what I'm trying to do, but I don't know how to get the basis polynomials, i.e. turning the middle section into the right section. I can probably get it to the interpolating section from there.
My points are as follows: 800, 175; 600, 125; 400, 100; 200, 125; 0,0; -200, -125; -400, -100; -600, -125; -800, -175.
Eventually, I'm going to try and dynamically swap out the points above in the program I'm building, so I could really use a step by step description. I read Determining Coefficients of a Finite Degree Polynomial $f$ from the Sequence $\{f(k)\}_{k \in \mathbb{N}}$, but I don't quite follow it. It's very possible I'm out of my depth and should re-think what I'm trying to accomplish, but I'd really like to try this. Thanks!