Unisolvent Point Set

In approximation theory, a finite collection of points $X \subset R^n$ 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 $\Pi^m_n$ (polynomials in n variables of degree at most m) if there exists a unique polynomial in $\Pi^m_n$ 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 $\Pi^k$.

See also

*Padua points

External links

Numerical Methods / Interpolation

Approximation theory

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