Best method to be implimented

Having a couple of equations inside a function. This function has an output.This output is again an input in the same equation until the tolerence between the tolerence between last output and previous output have a certain value like 10e-4. This could be implimented with a while loop. Something like this i guess (still I didnt impliment it in MATLAB) :

y = 1
x= = fun(y)

while (y-x)>10e-4
   y=x
   x = fun(y)
end

Is there any other way?

[Guillaume]

The code you've shown will do what you've described and is probably the simplest.

The issue with your code and what you've described is that it may never converge (e.g. if fun(x) = -x), so rather what don't you say what you're trying to achieve.

Answer 1

[Matt J]

If fun(x) is continuous wrt x and the iterations you describe do converge to something, then the limit will satisfy

     x=fun(x)

which you can solve with fzero

    fzero(@(x) x-fun(x), x0)