unisolvent point set

{{unreferenced|date=August 2012}}

In approximation theory, a finite collection of points $X\; \backslash subset\; R^n$ is often called unisolvent for a space $W$ if any element $w\; \backslash in\; W$ is uniquely determined by its values on $X$.

$X$ is unisolvent for $\backslash Pi^m\_n$ (polynomials in n variables of degree at most m) if there exists a unique polynomial in $\backslash Pi^m\_n$ of lowest possible degree which interpolates the data $X$.

Simple examples in $R$ would be the fact that two distinct points determine a line, three points determine a parabola, etc. It is clear that over $R$, any collection of k + 1 distinct points will uniquely determine a polynomial of lowest possible degree in $\backslash Pi^k$.