a. Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced points

Question:

a. Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced points given in the following table:
x f (x)
−0.1 5.30000
0.0 2.00000
0.2 3.19000
0.3 1.00000
b. Add f (0.35) = 0.97260 to the table, and construct the interpolating polynomial of degree four.