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Thread: [SOLVED] Hermite Interpolating Polynomial

  1. #1
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    Joined
    Dec 2008
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    6

    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
    $\displaystyle
    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

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

    and

    $\displaystyle
    \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 $\displaystyle \tilde H_{n,j}(x)$ such that
    $\displaystyle
    \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...
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  2. #2
    Newbie
    Joined
    Dec 2008
    Posts
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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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