0 like 0 dislike
0 like 0 dislike
I don't understand iteration

3 Answers

0 like 0 dislike
0 like 0 dislike
Suppose you play a guessing game where someone thinks of a number, and then you try to guess it.  They tell you if your guess was too high or too low.

You can see that you can  eventually guess their number of any degree of precision.
0 like 0 dislike
0 like 0 dislike
Search "cobweb plot"
0 like 0 dislike
0 like 0 dislike
In fact, strictly speaking it doesn't always work. Whether it does or does not depends on the behavior of the function sufficiently close to the point you are trying to find the value at. Namely, the condition for iteration to work is that the function must "contract" a suitably small neighborhood of the desired fixed point x\_0 around that neighborhood. That is, if we have an interval half-width epsilon, then for every value of x in \[x\_0 - epsilon, x\_0 + epsilon\], f(x) e \[x\_0 - epsilon/A, x\_0 + epsilon/A\] (i.e. a shrunken interval, shrunk by the factor A) for a *fixed* downscaling factor A > 1 that is *independent* of epsilon, *provided* epsilon is smaller than some threshold. For a differentiable function, this condition corresponds to having |f'(x\_0)| < 1.

No related questions found

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!