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Curve fitting using (r, f(r), f'(r), f''(r))

  1. Oct 2, 2008 #1

    I know the value of a function f and its first and second derivatives at different point r (1D).

    I know how to fit it using only f(r) and r, but I'm sure its is possible to improve the quality/speed of the fitting by using also f'(r) and f''(r).

    Is anybody have in mind a fitting algorithm using all (r, f(r), f'(r), f''(r))?

    Any suggestion (book, web site, paper...) on this topic will be really appreciated.



    EDIT: The fitting probably needs a sum of gaussian type function.
  2. jcsd
  3. Oct 2, 2008 #2


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    You are right that knowledge of derivatives will improve the quality of the fit between your known points. The book Numerical Methods for Scientists and Engineers by Hamming devotes a chapter to doing exactly this. It is published by Dover and available cheaply.
    Last edited: Oct 3, 2008
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