Purpose
This app can be used to fit data to Chebyshev polynomial series of the first kind.
\(f(x)=A_{0}\times T_{0}(\bar{x})+A_{1}\times T_{1}(\bar{x})+...+A_{n}\times T_{n}(\bar{x})\)
Each polynomial is represented with normalized argument \(\bar{x}\) by the recurrence relation
\(T_{0}(\bar{x})=1\)
\(T_{1}(\bar{x})=\bar{x}\)
\(T_{n+1}(\bar{x})=2xT_{n}(\bar{x})-T_{n-1}(\bar{x})\)
Installation
Download the file, then drag-and-drop onto the Origin workspace. An icon will appear in the Apps gallery window.
Operation
- Activate a worksheet with XY/Y Error columns, or a graph page with data plots.
- Click the icon in the Apps Gallery window to open the dialog.
- Select XY columns or data plots as input.
- Select another column as Y Error (optional). Then you can choose No Weighting, Direct Weighting or Instrumental as how you want to treat errors as weight.
- Choose polynomial order.
- Click Preview or check Auto Preview to view fitted curve.
- Specify quantities and plots to output.
- Click OK.