(proof-reading through HN is a mildly embarrassing process, sorry about that! I do go over these posts and proof-read them several times myself before publishing)
The Lagrange polynomials form the normal basis of most Finite Elements Method (FEM) software. There are other polynomials which are used as well, but these are the workhorse of most solvers.
the last matrix before the appendix is not the identity matrix, right now the matrix is: \begin{bmatrix}
1 & 0 & 0 & \dots & 0\\
1 & 0 & 0 & \dots & 0\\
1 & 0 & 0 & \dots & 0\\
\vdots & \vdots & \vdots & \ddots &\vdots \\
1 & 0 & 0 & \dots & 1
\end{bmatrix}
In the Polynomial Interpolation Theorem, you have r(x) = p(x) - r(x), but I think it should be q(x) = p(x) - r(x).
Fixed, thank you! (it's actually r(x)=p(x)-q(x))
(proof-reading through HN is a mildly embarrassing process, sorry about that! I do go over these posts and proof-read them several times myself before publishing)
The Lagrange polynomials form the normal basis of most Finite Elements Method (FEM) software. There are other polynomials which are used as well, but these are the workhorse of most solvers.
the last matrix before the appendix is not the identity matrix, right now the matrix is: \begin{bmatrix} 1 & 0 & 0 & \dots & 0\\ 1 & 0 & 0 & \dots & 0\\ 1 & 0 & 0 & \dots & 0\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & 0 & 0 & \dots & 1 \end{bmatrix}
Thanks for noticing, I'll fix it shortly