IN WHAT SENSE IS THE RATIONAL INTERPOLATION PROBLEM WELL POSED

It is well known that the nonlinear problem of interpolating m+n+1 data by a rational function of type (m, n) may have no solution, but that the corresponding linearized problem (obtained by multiplying through by the denominator) always leads to a unique rational function, which is often still called the rational interpolant. For fixed m and n, and fixed (possibly multiple) interpolation points, the dependence of this interpolant on the prescribed function values is studied here. For ten notions of convergence in the space ℛm, n the question of the continuity of this interpolation operator is investigated. © 1990 Springer-Verlag New York Inc.