How Are Lagrange Polynomials Computed and Proven?

[e.gedge]

Lagrange Polynomals are defined by:

l_j(t)= (t-a₀) ...(t-a_j-1)(t-a_j+1)...(t-a_n) / (a_j-a₀)...(a_j-a_j-1)(a_j-a_j+1)...(a_j-a_n)

A) compute the lagrange polynomials associated with a₀=1, a₁=2, a₂=3. Evaluate l_j(a_i).

B) prove that (l₀, l₁, ... l_n) form a basis for R[t] less than or equal to n.

C) Deduce the Lagrange interpolation formula.

Thanks!

 

[IDimitrov]

I suggest that rather than asking for help on my homework assignments in a forum where it specifically states "this is not for homework" that you instead come to the tutorials.