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Math Help - [SOLVED] Hermite Interpolating Polynomial

  1. #1
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    Dec 2008
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    Unhappy [SOLVED] Hermite Interpolating Polynomial

    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
    <br />
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)<br />

    where

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

    and

    <br />
\hat H_{n,j}(x) = (x-x_j)L^2_{n,j}(x)<br />

    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
    <br />
\tilde H''_{n,j}(x_i) = \begin{cases}<br />
				1 &\text{ if } i=j\\<br />
				0 &\text{ otherwise}<br />
			\end{cases}<br />


    I would love to know if you could offer any help. I'm stumped...
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  2. #2
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    Joined
    Dec 2008
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    Well, found my answer here.

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