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

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SUMMARY

This discussion focuses on enhancing curve fitting techniques by incorporating function values, first derivatives, and second derivatives at various points. The user seeks an algorithm that utilizes all four components: (r, f(r), f'(r), f''(r)). It is established that using derivatives improves the fitting quality and speed. The book "Numerical Methods for Scientists and Engineers" by Hamming is recommended as a resource that addresses this topic in detail.

PREREQUISITES
  • Understanding of curve fitting techniques
  • Familiarity with derivatives in calculus
  • Knowledge of Gaussian functions
  • Basic programming skills for implementing algorithms
NEXT STEPS
  • Research algorithms for curve fitting that utilize derivatives
  • Study the chapter on curve fitting in "Numerical Methods for Scientists and Engineers" by Hamming
  • Explore Gaussian function fitting techniques
  • Learn about optimization methods for improving fitting accuracy
USEFUL FOR

Data scientists, mathematicians, and engineers involved in numerical analysis and curve fitting who seek to improve their fitting models using derivatives.

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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.
 
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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.
 
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