Gauss-Newton Solution for Nonlinear Regression

Using the initial guess for the parameters, fi, the grand Jacobian matrix is evaluated, and the predicted values are determined. 

the difference between the predicted values, y, and the actual, measured values is determined, that is. 

Using an appropriate numerical method, the following system of equation is solved for A,  

The new value of the parameters,, then becomes the new guess, and the above procedure is repeated from Step 1. This procedure continues until the difference in values between the parameters from two consecutive steps is less than some predetermined accuracy, or a certain number of iterations has been reached. 

As with many numerical methods, the following are some common issues  

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