Mastering While Loops in Mathematica for Newton's Method Calculations

[AxiomOfChoice]

I am trying to do some Newton's method-type stuff in Mathematica.

I want to build a While loop that does the following:

- Take input r.
- Compute some quantity f(r).
- Update the value of r to f(r).

- Repeat until |g(r)| < C for some fixed constant C.

The third (boldfaced) step is the one I'm having trouble with. I don't know how to do this. Can someone help?

 

[Bill Simpson]

Something like this?

f[r_]:=r^2;
g[r_]:=r-1/100;
c=1/20;
r=Input["What's r?"];(*Enter something between -1 and 1 *)
While[Abs[g[r]]>c,
r=f[r];
Print[r]
]

If that doesn't give you enough then we need to see what you have already done