Unisolvent point set

Summary

Let $V$ be a finite-dimensional space of functions. A set of points is unisolvent for $V$ when each choice of values at the points is taken by exactly one function in $V$. It is the condition under which an interpolation problem has a unique answer. In one variable, any $n + 1$ distinct points are unisolvent for the polynomials of degree at most $n$, which is the basis of polynomial interpolation. In several variables the position of the points matters, and choosing unisolvent sets is a central problem of multivariate interpolation.