 Interpolation node

An interpolation node is an argument value $x_i$ at which an interpolation polynomial must take a prescribed value $y_i$. The interpolation nodes specify where the constraints apply; the values specify how high the graph must pass there. In the three-point example, the interpolation nodes are $0,1,2$, while the prescribed values are $1,2,5$. Changing the interpolation nodes changes the Lagrange cardinal polynomials and the polynomial interpolation error, even if their number stays fixed.