a. Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced points given in the following table:
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 x0, x1, … xn, for the function f:
INPUT numbers x0, x1, … xn; values f(x0), f(x1), …, f(xn) as F0,0, F1,0, …, Fn,0.
OUTPUT the numbers F0,0, F1,1, …, Fn,n where
Step 1 For i = 1, 2, …, n
For j = 1, 2, …, i
set
Step 2 OUTPUT (F0,0, F1,1, …, Fn,n);
STOP.
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