Background:
The example serves to illustrate surface fitting, in this case by a rational
function depending on fourteen
unknown parameters a_{1}, ..., a_{14} and two
independent variables x_{1} and x_{2}.
The Mathematical Model:
The fitting criterion is given in the form
a = a_{1}/x_{1}^{3} + a_{2} + a_{3}/x_{1}^{2} + a_{4}/x_{1} + a_{5}*x_{1} + a_{6} x_{1}^{2} + a_{7}*x_{1}^{3} + a_{8}*x_{2}^{2} + a_{9}*x_{2} + a_{10}/x_{2}^{2} + a_{11}*x_{12}*x_{2} + a_{1}2*x_{1}*x_{2}^{2} + a_{13}/(x_{1}^{2}*x_{2}) + a_{14}*x_{2}^{3}
The parameters x_{1} and x_{2
}are scaled.
Implementation:
The complete solution of a data fitting problem is described
in six
steps:
Results:
Then you would like to take a look at reports and graphs:
- parameter values
- experimental data versus fitting criterion
Model equations (or use your own favorite editor):
Measurement data (or use import function for text file or Excel):
Parameters, tolerances and start of a data fitting run:
Numerical results (computed by the least squares code DFNLP):
Report on parameter values, residuals, performance, etc. (or export to Word):
Experimental data versus fitting criterion (also available for Gnuplot):