Generalized Inverse Vector Valued Osculatory Rational Interpolation and Its Error Formula

In this paper, osculatory rational functions of Thiele-type introduced by Salzer (1962) are extended to the case of vector valued quantities using tile t’ormalism of Graves-Moms (1983). In the computation of the osculatory continued h.actions, 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 sutficient condition for cxistence is established. Some interpolating properties including uniqueness are discussed. In the end, all exact interpolating error formula is obtained.