Interpolation of rational functions by simple partial fractions

Abstract

We study a generalized interpolation of a rational function at n nodes by a simple partial fraction of degree n and reduce the consideration to the solvability question for a special difference equation. We construct explicit interpolation formulas in the case where the equation order is equal to 1. We show that for functions A(x − a) m , $ m \in \mathbb{N} $ , it is possible to reduce the consideration to a system of m + 1 independent first order equations and construct explicit interpolation formulas. Bibliography: 6 titles.