Unisolvent point set

In approximation theory, a finite collection of points $X\subset \mathbb {R} ^{n}$ is often called unisolvent for a space $W$ if any element $w\in W$ is uniquely determined by its values on $X$.
$X$ is unisolvent for $\Pi _{n}^{m}$ (polynomials in n variables of degree at most m) if there exists a unique polynomial in $\Pi _{n}^{m}$ of lowest possible degree which interpolates the data $X$.

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

See also

• Padua points

External links

• Numerical Methods / Interpolation