1.25 Chebyshev Polynomial Fit

Summary

This Chebyshev Polynomial Fit App can be used to fit data to Chebyshev polynomial series of the first kind. \(f( x ) = A_{0} *T_{0}( \overline{x} ) + A_{1}*T_{1}( \overline{x} )+....+A_{n}*T_{n}( \overline{x} )\)

Each polynomial is represented with normalized argument \(\overline{x}\) by the recurrence relation
\(T_{0}( \overline{x} )=1\)
\(T_{1}( \overline{x} )=\overline{x}\)
\(T_{n+1}( \overline{x} ) = 2\overline{x}T_{n}( \overline{x} )-T_{n-1}( \overline{x} )\)

Tutorial

1. New a workbook and import ..\Samples\Curve Fitting\Gaussian.dat. Set Col(C) as Y Error.
2. Select the whole sheet and open Chebyshev Polynomial Fit.
3. You can choose No Weighting, Direct Weighting or Instrumental as how you want to treat errors as weight.
4. Choose polynomial order.
5. Click Preview or check Auto Preview to view fitted curve.

   

6. Specify Quantities and Plots to output. Click OK.