Interpolating Integral Continued Fraction of the Thiele Type

Abstract

We generalize the well-known results on the interpolation of a function of single variable by the Thiele–Hermite fraction with arbitrary multiplicity of each interpolation node to the case of a functional acting from the space of piecewise continuous functions with finitely many discontinuities of the first kind. We obtain an interpolating integral fraction of the Thiele type on the set of interpolation nodes one of which is continual. We also indicate an efficient approach to the construction of interpolating integral fraction of the Thiele type in the case where all interpolation nodes are continual. This case is important to balance the data used for the construction of the interpolant and its interpolating properties.