Subresultants, Sylvester sums and the rational interpolation problem.

D'ANDREA, CARLOS; KRICK, TERESA; SZANTO, AGNES

Frankfurt

Congreso; Effective Methods in Algebraic Geometry, MEGA'13; 2013

We present a solution for the classical univariate rationalinterpolation problem by means of (univariate) subresultants. In thecase of Cauchy interpolation (interpolation without multiplicities), werecover explicit formulas for the solution in terms of symmetric functionsof the input data, hence generalizing the well-known formulas for La-grange interpolation. In the case of the osculatory rational interpolation(interpolation with multiplicities), we get determinantal expressions interms of the input data.