Tasked with writing a MATLAB script that computes the Hermite interpolation of a function.
Specifically, it asks to find: $$p(x)\in \Pi_{2n+1} \text{, such that } p(x_0)=f(x_0), p'(x_0)=f(x_0)... ,p(x_n)=f(x_n),p'(x_n)=f'(x_n)$$
Can anyone explain what $p(x)\in\Pi_{2n+1}$ means with respect to this application?
Okay, this makes sense. Now the problem I'm having is different.
Probably it means that $p$ should be a polynomial of degree at most $2n+1$ (which makes sense, since you have $2n+2$ conditions).