Computation of rational interpolants with prescribed poles
The paper deals with the rational interpolant \(R_{M,N}\), \(M\geq 0\), \(N\geq 0\), belonging to the set of rational functions \({\mathcal R}_{M,N}\) and having N prescribed poles. A constructive proof for the existence and uniqueness of \(R_{M,N}\) that interpolates \(M+1\) Hermite data is given. It is based on explicit computation of the Cauchy-Vandermonde determinant in terms of nodes and poles. The proof constitutes the basis for the derivation of an algorithm computing the interpolant numerically. The computation scheme is described.
scientific article; zbMATH DE number 4117727