Saturday, March 17, 2018

Least Squares Parameter Fit for the Catenary


 This iterative correction for the fit of the parameters for the catenary using the least squares gradient formula works quite well too. The equations of condition for xmin and L are fairly smooth over a wide range as these grid plots show.



And the iteration of the corrections converges rapidly to the optimal values of xmin and L using an  initial rough estimate of their values.


Using the formulas for the catenary we can now compute exact values for ymin and y(b).


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