For the cubic spline interpolation if we have
A=(x2-x)/h; B=(x-x1/h); C=1/6*(A^3-A)*h^2; D=1/6*(B^3-B)*h^2;
y=A y1 + B y2 + C y1'' + D y2''
What is the interpolation error of above?
For example for Hermitian cubic spline it is smaller than 5/384 ||f^{(4)}|| h^4