HP calcs are really not that accurate..

[AlexFekken]

(12-04-2017 02:38 AM)Thomas Okken Wrote:  Yes, certain conditions have to be met in order for convergence to be guaranteed. That's high-school math. What changes when you calculate with intervals?

You need to add an essential additional requirement: that the starting interval contains the solution/fixed point. Of course if you have such an interval then bisection or a combination of bisection and Newton would also garantee convergence to a solution.

But I am not sure why the 'Starting point enters a cycle' situation could not occur and prevent convergence. Perhaps someone should try f(x)=x^3-2x+2 with an interval that includes 0 and 1...

(Thinking a bit more) since 0 is mapped to 1 and 1 to 0 they will be in every iteration of the interval. I think that disproves it: interval-Newton does not necessarily converge either.