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# Modules

Curve fitting (linear and nonlinear)
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# Curve fitting (linear and non-linear)

A number of least squares curve fitting methods can be selected:

# Levenberg-Marquardt (non-linear) Curve Fitting

The example given below illustrates a fit to data from a Fermi distribution:

This example is made in the following steps

• The Function was defined and drawn for constant values: a=4, b=0.5, c=2

• Data points were read into the data grid by clicking on the graph (after pushing the "Read data from the graph" button in the Extra tab on the Data panel)

• Go back to the Function panel and select the constants (in this case a, b and c) for which you want to find a least squares solution to the data. Give them an appropriate initial value.
Note that you may select more than one constant by using the Ctrl or Shift Button.

• Select the Data from the Data grid and plot them

• Finally open the Curve Fitting panel, select Levenberg-Marquardt and press Go. The resulting solution is
drawn in the graph and the results together with some statistics of the residuals are shown in the Results window.

• Check to see if the original values of a and b and c are retrieved!!

Non-continuous functions or complicated periodic functions are difficult to fit. Such functions require
special fitting algorithms. As an experiment define and plot the singular function 1/(x+b) for b = - 5 in
the interval [0,10]. Read some points from the graph and try to find a fit with Levenberg-Marquardt.
Then try to fit it with the 4th or 5th entry in the Curve Fitting list box.

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