Finding roots of an equation {resolved}

[wossname]

I need to write an algorithm that can find the roots of any equation (of the form y=f(x).

It would have to do it by testing X values at certain points and homing in on the root by finding the sign change. What is the most efficient method of doing this?

[azteched]

Are you considering equations with complex roots too?

e.g.

(x^2) = -2

"Any" equation is quite broad.

[wossname]

Not complex ones no. Only Y=0 (for now)

OK, not ANY curve then

I'm not doing this by re-arranging equations or any cheating like that, just by calculating the Y at certain X values and interpolating to find roots.

Function Get_Y_Value(x) 'can be treated as a "black box", we don't need to know the equation itself.

[azteched]

So you'll need some sort of heuristic method to produce a reasonable guess at a root, then decrease or increase x depending on whether you're too high or low.

You can scale the increase or decrease amount according to how far from y=0 you are, i.e. decrease the change as you approach y=0.

As for the initial guess, hmm..I don't know really. It probably doesn't matter if your guess is a long way off anyway as long as you use the change-scaling approach..

Also are you going to allow equations with no roots and detect that?

[wossname]

Its OK. I have sorted it out now. Cheers.