[SOLVED] Hermite Interpolating Polynomial

larley · #1 $Old$ December 18th, 2008, 10:32 PM

I saw a previous thread that was related, but it seemed to be missing some information, and it was never solved.

I know that for Hermite interpolation, every textbook has
$K_{2n+1}(x) = \sum_{j=0}^n f(x_j) H_{n,j}(x) + \sum_{j=0}^n f'(x_j) \hat H_{n,j}(x)$

where

$H_{n,j}(x) = [1 - 2(x-x_j)L'_{n,j}(x_j)]L^2_{n,j}(x)$

and

$\hat H_{n,j}(x) = (x-x_j)L^2_{n,j}(x)$

But how do I make it to the next step? What's the 3rd term, if I'm looking for $\tilde H_{n,j}(x)$ such that
$\tilde H''_{n,j}(x_i) = \begin{cases} 1 &\text{ if } i=j\\ 0 &\text{ otherwise} \end{cases}$

I would love to know if you could offer any help. I'm stumped...

larley · #2 $Old$ December 20th, 2008, 03:59 PM

Well, found my answer here.

I'll get back to you with any more questions plaguing me.