In mathematics and statistics, the curve fitting problem is how to choose from an infinite number of curves the one which fits best the given data points, normally by finding a mathematical expression to create the curve.

The simplest curve is considered preferable. This is thought to be related to Occam's Razor in so far as there is a preference for simplicity among a family of curves just as there is a preference for simplicity among competing theories.

Commonly used procedures are least squares fitting, linear regression, and nonlinear regression. One of the difficulties in curve fitting is to choose the functional form of the data for parameter optimization. Computers are normally used to perform curve fitting procedures and they do this by solving a system of equations to find the parameters of the function that minimize the squared error. Frequently used methods are the gradient descent algorithm, the Gauss-Newton algorithm, and the Levenberg-Marquardt algorithm.

Probabilistic algorithms such as RANSAC can be used to find a good fit for a sample set, given a parametrized model of the curve function.

References

Audi, R., Ed. (1996) The Cambridge Dictionary of Philosophy. Cambridge, Cambridge University Press. curve fitting problem p.172-173.

External links

• Curve Expert (shareware) http://www.ebicom.net/~dhyams/cftp.htm fits functions to data (limited to one dependant and one independent variable.)
• Online curve and surface fitting http://zunzun.com
• TableCurve2D and TableCurve3D by Systat http://www.systat.com automates curve fitting
• LMS applet http://intrepid.mcs.kent.edu/~blewis/stat/lsq.html
• another choice http://www.softintegration.com/chhtml/lang/lib/libch/numeric/CGI_Curvefit.html
• online curve-fitting textbook http://curvefit.com/