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\(

\left(\frac{\sum_{i=1}^{n}y_i \frac{x_i}{k+x_i}}{\sum_{i=1}^{n}(\frac{x_i}{k+x_i})^2}\right)\sum_{i=1}^{n}\left[ \left(\frac{x_i}{k+x_i} \right)\left( \frac{x_i}{(k+x_i)^2}\right)\right ]-\sum_{i=1}^{n}\left(y_i\frac{x_i}{(k+x_i)^2} \right)

\)

with respect to k (i.e. \(\frac{\partial }{\partial k}\)). I know mathematica and maple should be able to do this, but don't have the software. Can someone please run this for me to get the derivative???

http://www.stat.berkeley.edu/classes/s243/nlin.pdf

http://web.itu.edu.tr/~msahin/mat202e/Answer#4.pdf

I took the problem as saying that we were allowed to implement the model-equation and its partial derivatives (with respect to the parameters to be estimated) as functions in C. (That is, we could just calculate the partials by hand and code them in directly. You could use Mathematica if you want to, but it seems like overkill.) We would then be able to call those functions to compute things like the residuals or the i,jth element of the Jacobian.

The hardest part for me was figuring out how to accommodate an arbitrary number of parameters, observations, and independent variables in my program. I ended up using a function pointer for the model-equation and an array of function pointers to store the partial derivatives. This might not be the best way to approach the problem, but it worked for me.

I'm going to go collapse now, but I'll try to check in this afternoon to see if you have more questions. Good luck!!

(late, really late)

All it means by half-stepping is to try half the iteration step if the actual iteration step yields values of the parameters that give a larger sum-of-squared residuals.

All it means by half-stepping is to try half the iteration step if the actual iteration step yields values of the parameters that give a larger sum-of-squared residuals.

One last bit of advice: I found this method to be pretty sensitive to the initial values.