Definition
Given a set of n + 1 data points (xi,yi) where no two xi are the same, one is looking for a polynomial p of degree at most n with the property
The unisolvence theorem states that such a polynomial p exists and is unique, and can be proved by the Vandermonde matrix, as described below.
The theorem states that for n+1 interpolation nodes (xi), polynomial interpolation defines a linear bijection
where is the vector space of polynomials (defined on any interval containing the nodes) of degree at most n.
Read more about this topic: Polynomial Interpolation
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