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Newtons Divided Difference First Derivative

  1. Feb 28, 2016 #1
    Hey all, for a function approximation program t run fast enough i need to solve for where the function (represented by a NDDP) is at a minimum (necessary trust me), althogh I have no idea how to go about differentiating it, i tried to break it up from its's general formula (the pi operators and the sigma summations make the differentiation difficult for me as i have never had to differentiate a pi operator before), but that seems to make things worst is the first derivative for a nth order NDDP known? Any help apreciated.
     
  2. jcsd
  3. Feb 28, 2016 #2

    BvU

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    2.2 here perhaps ? Or did you find that already ?
     
  4. Feb 28, 2016 #3
    Thanks :D
     
  5. Feb 29, 2016 #4
    Wasnt familiar with the reccurance relation version so that paper didn't help too much, however found a nice pattern, turns out the derivative is

    $$ \sum_{k=0}^{k<=n}\sum_{i=0}^{k} \Pi_{j=0, j \neq i}^{k-1} (x-x_j) $$

    You can see it in action here for 4th order poly
     

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