Numerical Analysis, 9th ed Burden.

Use STRICTLY the next algoritm to make Newtons Divided-Difference Formula method code in Python:

Use this Newtons Divided-Difference Formula Python program to get the same Output Table below of the next Illustration:

(Points are: 1.0, 1.3, 1.6, 1.9, 2.2) The function f is: f(1.5)

ALGORITHM 3.2 Newton's Divided-Difference Formula To obtain the divided-difference coefficients of the interpolatory polynomial P on the (n+1) distinct numbers Xo, X1, ..., Xn for the function f: INPUT numbers Xo, X1, . . . , Xn; values f (xo), f (xi),..., f (xn) as F0,0,F1,0,...,F1,0. OUTPUT the numbers F0,0, F1,1,...,Fn,n where i-1 P..(x) = F0,0 + Fii/[(x x;). (Fij is f[xo,X1,..., Xi].) i=1 j=0 Step 1 For i = 1,2,...,n For j = 1, 2, ..., Fij-1 Fi-1.j-1. (Fij = f[xi-j,. .. , Xi].) set Fij Xi - Xi-j Step 2 OUTPUT (F0,0, F1,1, ..., Fn,n); STOP. Table 3.11 i X; f[x] f [x;-1,x;] f[x;-2,Xi-1,x;] f[x;3, ...,x;] f[x;-4,...,x;] 0 1.0 0.7651977 -0.4837057 1 1.3 0.6200860 -0.1087339 -0.5489460 0.0658784 2 1.6 0.4554022 -0.0494433 0.0018251 -0.5786120 0.0680685 3 1.9 0.2818186 0.0118183 -0.5715210 4 2.2 0.1103623