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a guest Jun 27th, 2019 71 Never
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  1. from scipy import *
  2. import numpy as np
  3. from numpy import array
  4. from scipy import integrate
  5. import matplotlib.pyplot as plt
  6. import scipy.integrate as si
  7. from scipy.optimize import fsolve
  8. from math import log
  9. import matplotlib as mpl
  10. import itertools
  11.  
  12.  
  13. def applog(n,x):
  14.     a0=(1+x)/2
  15.     b0=sqrt(x)
  16.  
  17.     for i in range(n):
  18.         a0=(a0+b0)/2
  19.         b0=sqrt((a0)*b0)
  20.    return (x-1)/a0
  21.  
  22. def Euler_accelerate(sequence):
  23.  
  24.     s0 = next(sequence)
  25.     s1 = next(sequence)
  26.     s2 = next(sequence)
  27.     while True:
  28.         yield s0 - ((s1 - s0)**2)/(s2 - 2*s1 + s0)
  29.         s0, s1, s2 = s1, s2, next(sequence)
  30.  
  31.  
  32. x = np.linspace(10, 500, 100)
  33. nn=range(1,6)
  34. colors = mpl.cm.rainbow(np.linspace(0, 1, len(nn)))
  35.  
  36.  
  37. for c,n in zip(colors,nn):
  38.     print(itertools.islice(Euler_accelerate(applog(n,x)), 10))
  39.     plt.plot(itertools.islice(Euler_accelerate(applog(n,x)), 10))
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