In approximation theory, a finite collection of points X ⊂ R n {\displaystyle X\subset \mathbb {R} ^{n}} is often called unisolvent for a space W {\displaystyle W} if any element w ∈ W {\displaystyle w\in W} is uniquely determined by its values on X {\displaystyle X} .
X {\displaystyle X} is unisolvent for Π n m {\displaystyle \Pi _{n}^{m}} (polynomials in n variables of degree at most m) if there exists a unique polynomial in Π n m {\displaystyle \Pi _{n}^{m}} of lowest possible degree which interpolates the data X {\displaystyle X} . Simple examples in R {\displaystyle \mathbb {R} } would be the fact that two distinct points determine a line, three points determine a parabola, etc. It is clear that over R {\displaystyle \mathbb {R} } , any collection of k + 1 distinct points will uniquely determine a polynomial of lowest possible degree in Π k {\displaystyle \Pi ^{k}} .
See also Padua points
External links Numerical Methods / Interpolation