Is it unreasonable to interpolate between these higher degree polynomials?
OtB_BlueBerry
The error for degree-n polynomial interpolation (with (n+1) nodes) is given by an (n+1)-th order derivative at some x. In this case, the higher-order derivatives of the Runge function blow up too fast (faster than n!). As a consequence, the interpolation error blows up as n increases.
Is it unreasonable to interpolate between these higher degree polynomials?
The error for degree-n polynomial interpolation (with (n+1) nodes) is given by an (n+1)-th order derivative at some x. In this case, the higher-order derivatives of the Runge function blow up too fast (faster than n!). As a consequence, the interpolation error blows up as n increases.
https://en.wikipedia.org/wiki/Polynomial_interpolation#Interpolation_error
https://en.wikipedia.org/wiki/Runge's_phenomenon