Interpolant
= Interpolant
{title2=$g(x_i)=y_i$}
An interpolant is a <function> satisfying the prescribed sample conditions $g(x_i)=y_i$. It agrees with the data exactly, but need not agree with an unknown underlying function between samples. The <polynomial interpolation> example shows that a family or a <polynomial degree> restriction can supply uniqueness; the <McShane extension theorem> shows a useful nonunique alternative.