Generalized inverse vector valued osculatory rational interpolation and its error formula

Abstract

In this paper, osculatory rational functions of Thiele-type introduced by Salzer (1962) are extended to the case of vector valued quantities using the formalism of Graves-Morris (1983). In the computation of the osculatory continued fractions, the three term recurrence relation is avoided and a new coefficient algorithm is introduced, which is the characteristic of recursive operation. Some examples are given to illustrate its effectiveness. A sufficient condition for existence is established. Some interpolating properties including uniqueness are discussed. In the end, an exact interpolating error formula is obtained.