Lagrange Form (Interpolation)
The lagrange basis is a different basis for interpolating polynomials.
We will define the Lagrange basis functions, , to construct a polynomial as where are the coefficients (and are also our data values, .
Why use Lagrange form over a Vandermonde System?
One advantage of the Lagrange form is that the interpolating polynomial can be written down directly, without needing to solve a (Vandermonde) linear system.