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Newton's Interpolation, numerical methods question

  1. Nov 12, 2007 #1
    Can anyone tell me what is the equation for First Order of Newton’s Interpolation?

    The one of Interpolation I know is Lagrange’s Interpolation such as

    [tex]p(x)= \frac {x-x1}{x0-x1} f(x0) + \frac {x-x0}{x1-x0} f(x1)[/tex]

    and so on ...

    Thanks in advance
     
  2. jcsd
  3. Nov 17, 2007 #2
    well...

    well, i don't have math type on this computer, so you will have to bear with me, but:

    the nth term is found by dividing the function evaluated at the n-1th term by the derivative of the function evaluated at the n-1th term and then subtracting that from the nth term.

    that's it!
     
  4. Nov 17, 2007 #3

    HallsofIvy

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    How can you find the nth term by subtracting something from the nth term?

    The only Newton Interpolation formula I know is "Newton's divided difference" formula- which does not involve finding derivatives. It's a bit complicated to write out but here is a good explanation from Wolfram:
    http://mathworld.wolfram.com/NewtonsForwardDifferenceFormula.html.

    As far as "first order" is concerned, it is just f(x)= f(x0)+ (f(x1)- f(x0))(x- x0)/(x1-x0). Which obviously takes on the correct values at x= 0 and x= 1 and linearly interpolates between. If you look closely you will see that it gives exactly the same values as Lagrange's formula: all linear interpolation schemes between two points are the same.
     
  5. Nov 17, 2007 #4
    good point.... should be subtracted from the n-1th term. bad typing on my part! thanks for noticing;-)
     
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