fixed point to find root of a²＋a³＝392 but report OverflowError

Question

I tried to find the root of a²＋a³＝392 with fixed_point introduced by SICP 1.1.3 functions as general method

#+BEGIN_SRC scheme :session sicp
(define tolerance 0.00001)

(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
    (< (abs (- v1 v2))
       tolerance))
  (define (try guess)
    (let ((next (f guess)))
      (if (close-enough? guess next)
          next
          (try next))))
  (try first-guess))
#+END_SRC

I rewrite it in python as:

#+begin_src ipython :session sicp :results output :tangle pySrc/sicp_fixedpoint.py
import math
tolerance = 0.00001

import math

def fixed_point(f, guess):
    while True:
        nex = f(guess)
        if abs(guess-nex) < tolerance:
            return nex
        else:
            guess = nex 

def f(x):
    return 392 / (x + x**2)
fixed_point(f, 1)
#+end_src

It report error:

 OverflowError: (34, 'Numerical result out of range')

What's the problem?

Answer 1

I think this problem is not well suited for solving via a fixed-point procedure. If you print the (abs (- next guess)) for each iteration, you'll see that the value is increasing between iterations, it'll never converge to the specified tolerance - hence the Numerical result out of range error.