Diferencias Dividicas de Newton en Python

#Diferencias Divididas de Newton

#Autor: Alexander Arias

#Fecha: 26 de octubre de 2018

import numpy as np

t=np.array([4.0,6.0,2.0,8.0])

p=np.array([116.0,74.0,62.0,8.0])

A=np.zeros((4,4),float)

A[:,0]=p[0:4]

print(A[:,0])

A[1,1]=(A[1,0]-A[0,0])/(t[1]-t[0])

A[2,1]=(A[2,0]-A[1,0])/(t[2]-t[1])

A[3,1]=(A[3,0]-A[2,0])/(t[3]-t[2])

#print('--------------------------')

A[2,2]=(A[2,1]-A[1,1])/(t[2]-t[0])

A[3,2]=(A[3,1]-A[2,1])/(t[3]-t[1])

#print('--------------------------')

A[3,3]=(A[3,2]-A[2,2])/(t[3]-t[0])

#print('--------------------------')

print(A)

​

for k in range(1,4):

        for i in range(k,4):

            A[i,k]=(A[i,k-1]-A[i-1,k-1])/(t[i]-t[i-k])

print(A)

[ 116.   74.   62.    8.]
[[ 116.     0.     0.     0. ]
 [  74.   -21.     0.     0. ]
 [  62.     3.   -12.     0. ]
 [   8.    -9.    -6.     1.5]]
[[ 116.     0.     0.     0. ]
 [  74.   -21.     0.     0. ]
 [  62.     3.   -12.     0. ]
 [   8.    -9.    -6.     1.5]]