= Interpolation polynomial
{title2=$p(x_i)=y_i$}
An interpolation polynomial for distinct nodes $x_0,\ldots,x_n$ and prescribed values $y_0,\ldots,y_n$ is a <polynomial> $p$ satisfying $p(x_i)=y_i$. There is a unique such <polynomial> of degree at most $n$: the <Lagrange interpolation polynomial> constructs it explicitly, and uniqueness follows because a nonzero degree-at-most-$n$ difference cannot have $n+1$ distinct roots. <Newton interpolation polynomials> express the same object using <divided differences>.
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