Numerical Analysis, 9th ed Burden.

Use STRICTLY the next algoritm to make Nevilles Iterated Interpolation method code in Python:

Use this Same Nevilles Iterated Interpolation method code in Python program to get the same Output Table below of the next Illustration: (Points are: 1.0, 1.3, 1.6, 1.9 y 2.2, and the 2.5)

Remember that f '(x)=1/x !!

ALGORITHM 3.1 Neville's Iterated Interpolation To evaluate the interpolating polynomial P on the n + 1 distinct numbers xo),...,n at the number x for the function f: INPUT numbers X,X0,XI, ... ,( values f(xo), f(x)...., f (x) as the first column 20.0, Q1,0,...,Q... of Q. OUTPUT the table with P(x) = Qnre: Step 1 For i = 1,2, ..., for j = 1,2,..., set Oy (x - Ni-;) Qi.j-1 - (x - 2)Q-1.j-! Step 2 OUTPUT (Q): STOP Table 36 1.0 1.3 1.6 1.9 2.2 2.5 0.7651977 0.6200860 0.5233449 0.4554022 0.5102968 0.5124715 0.2818186 0.5132634 0.5112857 0.5118127 0.1103623 0.5104270 0.5137361 0.5118302 -0.0483838 0.4807699 0.5301984 0.5119070 0.5118200 0.5118430 0.5118277