It is well known-known that the interpolation error of a cubic spline has at best order $\mathcal{O}(h^4)$$O(h^4)$, which results from polynomials of degree 3.
Can I assume that if one uses polynomials of degree p and the respective function to be interpolated $f\in C^p([a,b])$, that the interpolation error of this spline is $\mathcal{O}(h^{p+1})$ ?
Is this known in Literature ? (I couldn't seem to find it$3$.)
Can I assume that, if one uses polynomials of degree $p$ and the respective function to be interpolated $f\in C^p([a,b])$, that the interpolation error of this spline is $O(h^{p+1})$? Is something like this present in literature?
