python - fixed point iteration algorithm -

i asked write program solve equation ( x^3 + x -1 = 0 ) using fixed point iteration.

what algorithm fixed point iteration? there fixed point iteration code sample in python? (not function modules, code algorithms)

thank you

first, read this: fixed point iteration:applications

i chose newton's method.

now if you'd learn generator functions, define generator function, , instance generator object follows

def newtons_method(n):     n = float(n)  #force float arithmetic     nplusone = n - (pow(n,3) + n - 1)/(3*pow(n,2) +1)     while 1:         yield nplusone         n = nplusone         nplusone = n - (pow(n,3) + n - 1)/(3*pow(n,2) +1)  approxanswer = newtons_method(1.0)   #1.0 can initial guess... 

then can gain successively better approximations calling:

approxanswer.next() 

see: pep 255 or classes (generators) - python v2.7 more info on generators

for example

approx1 = approxanswer.next() approx2 = approxanswer.next() 

or better yet use loop!

as deciding when approximation enough... ;)