(a) Determine the polynomial interpolant to the data
t 1 2 3 4
p(t) 11 29 65 125
using the monomial basis.
(b) Determine the Lagrange polynomial interpolant to the same data and show that the resulting polynomial is equivalent to that obtained in part a.
(c) Compute the Newton polynomial interpolant to the same data using each of the three methods (triangular matrix, incremental interpolation, and divided differences) and show that each produces the same result as the previous two methods.