Barycentric form of polynomial interpolation undefined at $P(x_{j})$

Question

For example,

$P(0)$, $P(1)$, $P(2)$, $P(3)$ will be undefined because the denominator will be $0$. Does that mean we can't use barycentric form at $P(x_{j})$?

Answer 1

The barycentric form of the Lagrange interpolation formula is constructed in the way that it can be used only outside of the interpolation points $x_i$. For $x=x_i$ the value of function $f(x)$ is known anyway. So, in case of evaluation in the programming code one has to use "if/else".