Polynomial Interpolation

Unisolvence Theorem

Given $n$ data pairs $(x_i,y_i),i=1,\dots ,n$ with distinct $x_i$, there is a unique polynomial $p(x)$ of degree not exceeding $n-1$ that interpolates this data.

When there are very few points (<6), we do Polynomial Interpolation

• Vandermonde Matrix (monomial basis)
• Lagrange Form (Interpolation) (Lagrange basis)