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

[Tipi]

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.
TPEDIT: The fitting probably needs a sum of gaussian type function.

 

[marcusl]

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.