Newton Method

[Namir]

Davis' formula prevents division-by-zero overflow. That's one aspect. The second aspect is that when the derivative becomes (much) smaller than delta, the value of delta becomes more relevant and correction to guess x is non-zero, unless f(x) is also zero. I am not saying that Davis' method is fool-proof for each and every f(x). It's an enhancement to the original Newton's algorithm. Of course how well it works depends on the actual f(x), its roots, and the guesses you supply.

I don't use Davis' formula myself. I am just sharing my find, because I thought it had some merit.

Namir