I need to find the zero of a function $f(\lambda)$ which is of the form $\sum \frac{c_i^2}{(1+\lambda d_i)^2} -1 $. I tried using Newton's method, and it works sometimes, but it is higly dependent of the initial choice, and the chances of divergence are very high, since the function is "almost" flat.
What would be the best method to find the zero of such a function?
For now, I replaced Newton with secant method, and it seems to work better.