# Interpolation error of InterpolatingPolynomial[]

this is my first post so if I have any error while writing this, I'm sorry.

I had to do a polynomic interpolation for one of my lab experiments, and I need to get the error from it in order to continue. Any idea on how to do it?

This is the code:

f = {1.611 , 1.438 , 1.367 , 1.279 , 1.186 , 1.024 , 0.789 , 1.719 ,
1.815 , 1.921 , 2.041 , 2.360 , 2.831};
i = {0.0453, 0.0412, 0.0383, 0.0342, 0.0288, 0.0216, 0.0142, 0.0433,
0.0400, 0.0367, 0.0321, 0.0237, 0.0173};
datos = Transpose[{f, i}]
interp = InterpolatingPolynomial[datos, x];
Expand[interp]


I supose every parameter from the interpolation will have it's own uncertainty, but what I don't know is if Mathematica is able to show them all to me. Thanks in advance

• 5442.62 - 45353.6 x + 170957. x^2 - 385526. x^3 + 579400. x^4 - 611462. x^5 + 464716. x^6 - 256317. x^7 + 101841. x^8 - 28431.2 x^9 + 5294.38 x^10 - 590.532 x^11 + 29.8392 x^12 is wrong? This is my result for your code. Oct 25 '18 at 10:01
• Are you looking for an exact interpolation (as you did) of degree 12 ? Or are you looking for a polynomial approximation of your data p? Oct 25 '18 at 10:04
• "I suppose every parameter from the interpolation will have it's own uncertainty" -- There two sources, the round-off error in computing interp and the experimental error in f and i. I doubt a symbolic expression in terms of unknown individual errors in f and in i will be useful, but perhaps if the errors in f and i are each a known number or a known bound, then the uncertainty in the coefficients could be computed. Oct 25 '18 at 13:40

 Total[(((interp /. x -> #)  & /@ f) - i)^2]