I've used this is control systems where I wanted the square root of a signal. Given that the signal should not change quickly (may even have a low pass filter o

I've used this is control systems where I wanted the square root of a signal. Given that the signal should not change quickly (may even have a low pass filter on it) doing one iteration of this is much quicker than doing a regular square root computation each time step. Obviously, the usefulness of an approximation depends on what you're doing, but this does converge to the exact solution over time ;-)