2 ms·
The polynomial will go through your samples exactly, but you might have arbitrarily high error between the samples ( runges phenomenon), if your data is noisy a
by unlikelymordant 4y ago
The polynomial will go through your samples exactly, but you might have arbitrarily high error between the samples ( runges phenomenon), if your data is noisy at all it is much better to fit a low order polynomial to your data that minimises error. If your curve has no noise and you are free to choose the sample locations , minimax is the best way to guarantee minimum error between samples.
- Someone 4y agoIndeed. Computing the exact polynomial going through all noisy points also doesn’t make sense because adding or removing a data point wildly changes the polynomial. So, you can’t claim any of your polynomials really describes your problem. Even if your data isn’t noisy and the point added lies exactly on the previous polynomial (making the problem degenerate) chances are float rounding and numerical stability of your code can have that effect (https://arachnoid.com/polysolve/#x_limits https://arachnoid.com/polysolve/#x_limits)