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.
How can we know what degree of polynomials to use in a certain situation?
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)
Yes, it seems that few people use higher than cubic
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.