Cubic polynomial interpolation

Question

Problem:

Cubic polynomial interpolation

1. a) Consider the problem of cubic polynomial interpolation

                           p(xi) = yi, I = 0,1,23

with deg(p) < 3 and x0, x₁, x₂, x₃ distinct. Convert the problem of finding p(x) to another problem involving the solution of a system of linear equations.

b) Express the system from (a) in the form Ax = b, identify the matrix A and the vectors b and x.