I'm doing my project from numerical methods in math and I'm supposed to create the following program:
Inputs:
$n \in [0,\infty)$
a sequence $\Gamma_{i=0}^{n} (u_i) \in \mathbb{R}^{n+1}$ of x-coordinates to interpolate
a sequence $\Gamma_{i=0}^{n} (v_i) \in \mathbb{R}^{n+1}$ of y-coordinates to interpolate
Output:
- elements of sequence $\Gamma_{i=0}^{n} (a_i)$, which are coefficients of the interpolation of a polynome $L(x)= \sum_{i=0}^{n} > a_ix^i$, defines by the $(\Gamma_{i=0}^{n} (u_i), \Gamma_{i=0}^{n} > (v_i) )$
but I don't understand one thing:
From what I understand, I have to calculate the Lagrange polynomial. But what is the $n$ in the inputs and how should I include it in my calculations? Really not sure about that part. The lagrange polynome should always be the lowest degree possible, right? So why is the degree $n$ included as an input? I'm rather asking here than my prof, because I'm afraid that it's a stupid question.
EDIT: I think I understand now. The number $n$ is just the number of $x-y$ coordinates. Do I understand it correctly?
Thanks!