Polynomial Interpolation

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.