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

  1. Oct 2, 2008 #1
    Hi!

    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.

    Sincerely,

    TP


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

    marcusl

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    Science Advisor
    Gold Member

    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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