Numerical Analysis Using Sage by George A. Anastassiou & Razvan A. Mezei

Author:George A. Anastassiou & Razvan A. Mezei
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

If you wish, you can modify the previous code as follows, so it will print the entire table of divided differences.

#the array of data points given

points = [(2,1),(4,2),(8,3), (16,4)]

#we compute n from the size of the array

n = len(points)-1

#computes the set of divided differences

def PrintDividedDifferencesTable():

#create an array n+1 by n+1

divDiff = [[0 for i in range(n+1)] for i in range(n+1)]

#first column will contain the y values

#this is column 0!

for row in [0,1,2,..,n]:

divDiff[row][0]=points[row][1]

#compute, recursively the div differences

#one column at a time

#in second column will have f[.]

#in third column will have f[.,.], etc

for column in [1,2,..,n]:

#for a column, compute the value in each row

for row in [0,1, 2, .., n-column]:

divDiff[row][column]=(divDiff[row+1][column-1]

-divDiff[row][column-1])/(points[row+

column][0]-points[row][0])

for row in [0,1, 2, .., n]:

print points[row][0],"\t|", [ divDiff[row][column] for

column in [0,1,2,..,n-row]]

#call the function

PrintDividedDifferencesTable()

This will output

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