Interpolation of expression results in negative numbers with non-negative data.

Question

Hello,

I have some data that I use to initialize a Function which is non-negative. Upon interpolation, the Function contains negative values.

Can anyone explain or provide a reference for why this happens? Also, is there a nifty way to prevent this from happening without explicitly setting the negative values to zero?

Thanks!

Answer 1

Example: Assume you have data points (x, y): (-1, 0.5), (0.9, 0.31) and (1, 0.5) and try to fit a second order polynomial (y = f(x) ) to these (for instance f(x) = x^2 - 0.5) . Then, there are c such that f(c) < 0 for instance c = 0 even though all your y data are positive.

More information (like a minimal running code example) would be useful in order to provide more hints.