[CSC 335] Python Code from Class

[Andrew J. Pounds]

So I wanted to send you all the python code I used in class yesterday.  
For the fixed point method (using the inverse derived from Mathematica)

#!/usr/bin/python

def f(x):
   part1=(848.0 + 356.0*x + 27.0*x**2)**(1.0/2.0)
   part2=(178.0+27.0*x+3.0*3.0**(1.0/2.0)*part1)**(1.0/3.0)
   part4= 13.0*2.0**(1.0/3.0)/(3*part2)
   part5=part2/(3.0*2.0**(1.0/3.0))
   return part4+part5-4.0/3.0

x=100
for i in range(1,10):

    print x, f(x)
    x= f(x)

And then here is the code modified to use Steffenson's Convergence 
Algorithm.   I am not testing for convergence in either of these, but I 
am using them to quickly compute the sequence.   I really encourage 
those of you that are doing all of this by hand to give this a try.  
Althought there is a learning curve,  could really make your life easier.


#!/usr/bin/python

def f(x):
   part1=(848.0 + 356.0*x + 27.0*x**2)**(1.0/2.0)
   part2=(178.0+27.0*x+3.0*3.0**(1.0/2.0)*part1)**(1.0/3.0)
   part4= 13.0*2.0**(1.0/3.0)/(3*part2)
   part5=part2/(3.0*2.0**(1.0/3.0))
   return part4+part5-4.0/3.0

x=100
for i in range(1,10):

    p1 = f(x)
    p2 = f(p1)
    p  = x - (p1 - x)**2 / (p2 - 2.0*p1 + x)
    print x, p1, p2, p
    x=p


Let me know if you have any questions -- I'll do whatever I can.

-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj