Topics: Polynomial - Numerical Analysis

Let us have points , with when (i.e. all abscissas distinct).

We will build a polynomial of degree , called the Lagrange (interpolation) polynomial, that will allow us to interpolate this sequence of points.

Lagrange Basis


We define the Lagrange basis as the set of polynomials , where:

In particular, notice that:

  1. is of degree for all

(see Kronecker delta)

Lagrange Polynomial


We define the Lagrange (interpolation) polynomial as the linear combination:

This polynomial is special in that for all , . This happens thanks to the Kronecker delta-like behaviour of the polynomials in the basis.

This allows us to use the polynomial to interpolate the initial sequence of points.