Unattainable Points in Multivariate Rational Interpolation Original Research Article

The problem of unattainable points is typical for the case of rational interpolation. Having computed the rational interpolant p/q from "linearized" interpolation conditions, in other words, conditions expressed for fq−p instead of f−(p/q), it may occur that an interpolation point is also a common zero of p and q and hence that the rational function p/q is undefined in that interpolation point. Consequently the "nonlinear" interpolation condition cannot be satisfied in that interpolation point anymore, not even by the irreducible form of p/q. The interpolation point has become "unattainable."