Numerical solution w/o derivative
I know the function y = f(x).
I have observed the true y-value and want to find the x that it implies.
It is impossible to invert the function, i.e. to analytically solve for x=g(y).
The derivative of the function is unavailable, so I cannot use the Newton-Raphson method.
It isn't difficult to come up with a way of trial and error which work. But I want to check with you if there is some intelligent way to deal with such iterations in order to make the procedure reasonably efficient?
While it is possible to formulate the derivative of y=f(x), it is impractical to use it because it is a formula which fills an entire page! (According to Mathematica) I need to implement a way to solve this problem in c++.