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# In[1]:
import numpy as np
# In[2]:
C = 1/2
e0 = 0.1*np.random.rand()
rate = 1
# In[3]:
e = e0
for i in range(20):
print(e)
e = C*e**rate
# * What do you observe about the number of iterations it takes to decrease the error by a factor of 10 for `rate=1,2,3`?
# * Is there a point to faster than cubic convergence?
# ------------------
# Now let's see if we can figure out the convergence order from the data.
#
# Here's a function that spits out some fake errors of a process that converges to $q$th order:
# In[4]:
def make_rate_q_errors(q, e0, n=10, C=0.7):
errors = []
e = e0
for i in range(n):
errors.append(e)
e = C*e**q
return errors
# In[5]:
errors = make_rate_q_errors(1, e0)
# In[6]:
for e in errors:
print(e)
# In[7]:
for i in range(len(errors)-1):
print(errors[i+1]/errors[i])