I have an implicit function


which I want to call recursively, called initially with g=0. I have this working for a specified number of recursive calls rec.

h[x_, y_, z_, rec_] := Piecewise[{{f[x, y, z, 0], 
 rec == 0}}, f[x, y, z, h[x, y, z, rec-1];

Is there a neat way build a function keeps increasing rec until the change in h falls below a certain threshold?


  • 2
    $\begingroup$ Maybe FixedPoint would help. $\endgroup$
    – bill s
    Commented Apr 23, 2018 at 2:59
  • $\begingroup$ Perhaps NestWhile would be relevant $\endgroup$
    – user42582
    Commented Apr 23, 2018 at 6:02

1 Answer 1


Ah, I think I have my own answer, thanks to more reading...

h[x_, y_, z_] := Last[NestWhileList[f[x, y, z, #] &, 0, Abs[#1 - #2]/#2 > 0.01&, 2]] 

finds the answer with enough recursion for 1% accuracy.


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