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whdawn

How can we know what degree of polynomials to use in a certain situation?

dsaksena

We use mostly cubic ones to join 2 points because they give us enough freedom for a smooth joining.

Going too high leads to Runge Phenomenon (worsening because of too much oscillation of the curve)

whdawn

Yes, it seems that few people use higher than cubic

kmcrane

Right---one typically sticks with low-order polynomials in order to avoid oscillations, but there are polynomials specifically designed to avoid Runge's phenomenon, like the Chebyshev polynomials.