Lojzek
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Problem: We want to calculate a polynomial of degree N-1 that crosses N known points in the plane.
Solution A: solving a NxN system of linear equation (Gauss elimination)
Solution B: construction from Lagrange basis polynomials.
One of my professors said that the first solution is inferior and I am trying to find out why.
Of course method B is more explicit, but the required time for calculation of all coefficients is probably similar, since both methods require O(N^3) steps. Is there any difference in accuracy or any other reason that would make method B better?
Solution A: solving a NxN system of linear equation (Gauss elimination)
Solution B: construction from Lagrange basis polynomials.
One of my professors said that the first solution is inferior and I am trying to find out why.
Of course method B is more explicit, but the required time for calculation of all coefficients is probably similar, since both methods require O(N^3) steps. Is there any difference in accuracy or any other reason that would make method B better?