Choosing when to stop

We have said that when the slope becomes zero, we are done. However, in practical terms, because floating point hardware in computers is not infinitely accurate, we may not reach zero. Also, we may be happy with getting close enough, so we can stop early and make our algorithm faster. So in practice, we choose a tolerance, . If the absolute value of the slope is within the tolerance, we stop.

We choose carefully, based on our data.