, with initial guess
Using the following approximation:
, where is a step size on parameter
Wikipedia article says that you can solve this equation using Newton-Raphson method, which is basically a following iteration:
So, the question is how to correctly mix them together? What initial guess and function should be?
Also is quite complex in my case and I'm not sure if it possible to find another derivative of it analytically. I want to write an implementation of it by myself, so pblackefined Mathematica functions wouldn't work.