I need to compute the square roots of lots of numbers. The numbers increase monotonically by fixed step. For example, 1, 2, 3, ..., 1 000 000.
What is the fastest way to do so? Is it possible somehow to take the advantage of the growth and calculate the square roots incrementally?
I thought I would calculate the derivative and add it at each step. But the derivative contains again a square root so it doesn't help. Also, I don't mind to trade some precision for speed.