Fixed point iteration to solve f(x) = 0, using x = g(x).

itmax <-- ?
xtol <-- ?
ftol <-- ?

it <-- 0
xold <-- 0
x <-- initial value
old <-- 0
new <-- 0

Loop 

  it <-- it + 1
  xold <-- x
  x <-- g(x)
  old <-- new
  new <-- abs ( x - xold )

  if old is not 0, alpha <-- new / old, print alpha
    
  if new <= xtol and |f(x)| <= ftol, break from loop with success
  if it > itmax, break from loop with failure

End loop
  
Print x, f(x)