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Solvability of multivariate interpolation. (English) Zbl 0666.41003

An ordinary polynomial interpolation scheme is described by the admissible polynomials \(P(x)=\sum_{i\in S}a_ ix^ i\), \(x=(x_ 1,...,x_ s)\), \(i=(i_ 1,...,i_ s)\), \(s\geq 2\), where S is a lower set of lattice points i, and by the knot sets \(A_ q\subset S\), \(q=1,...,m\), which give the orders \(\alpha \in A_ q\) of the derivatives \(\partial P^{\alpha}/\partial x^{\alpha}\) to be interpolated at the q-th knot. The scheme is solvable for all selection of knots and data if and only if a proper Pólya condition is satisfied and if the sets \(A_ q\) are disjoint.
Reviewer: G.G.Lorentz

MSC:

41A05 Interpolation in approximation theory
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