How can we find the greatest difference between an interpolation of f and f itself? I assume that we would use the error in polynomial interpolation theorem, but how would we find the c in that case (i.e. f^(n+1) evaluated at c)?
We cannot, in general, find the ksi.
We can only find max of the derivative part and of the W part.
This is what is being done in tut07, q6.
How can we say about the upperbound of the error, if the max of the derivative part goes to infinity? (For example, in [0,1] the f(x)=x^(3/2) is not in C^2)
For the function f = x^(3/2) in [0,1],
you can say that f’’ goes to inf like x^(-1/2) with x → 0.
Depending what other terms or factors you have in the bound
next to f’’,
you may or may not be able to get a meaningful bound.
If the upper bound involves f’’ and h^2
and the function is f = x^(3/2) in [0,1],
then f’’ goes to inf like h^(-1/2) with h → 0,
and the bound converges to 0 like h^(3/2) with h → 0.