Hermite interpolation with symmetric polynomials (Q1681776)

A problem of Hermite interpolation for symmetric bivariate polynomials is solved, i.e. the problem to develop a symmetric bivariate polynomial of \(n\)-th degree which matches, on a set of distinct points, the function values and its partial derivatives. The authors construct a multipoint Berzolari-Radon set that solves the Hermite interpolation problem. The Berzolari-Radon set consists of distinct points distributed on lines. The points in the multipoint Berzolari-Radon sets are not necessarily distinct. The proof of the continuity property of the Hermite interpolation at the multipoint Berzolari-Radon set with respect to the interpolation points is given, too. To demonstrate the proposed solution of the Hermite interpolation problem, the paper is completed by several examples where a multipoint Berzolari-Radon set of degree 3 is constructed and the Hermite interpolation polynomial is computed. The suggested method can be applied in various areas of numerical analysis, digital signal processing, computer graphics, etc.