01 - Interpolation

Polynomials of Degree

Polynomials of Degree less than or equal to $n$ is

$${\Pi }_n=\{\text{real polynomials of degree}\le n\}$$

Polynomials Interpolating Data

Given data $f_i$ at distinct $x_i$ for $i=0,1,\cdots n$ with $x_0<x_1<\cdots <x_n$ then

Polynomial $p_n$ interpolates the data if

$$p_n(x_i)=f_i$$