Rational interpolation and the Euclidean algorithm

AbstractA general framework, leading to a parametrization of all rational functions which interpolate a given set of pairs of points, is investigated. This framework is based on the Euclidean algorithm. The resulting parametrization has the property that it keeps track of the complexity of both the numerator and of the denominator polynomials of the interpolating functions. The Cauchy interpolation problem and the related Padé approximation problem can be treated within this framework