A Neville-like method via continued fractions

As we know, the classical Nevilleʹs algorithm is an effective method used to solve the interpolation problem by polynomials. In this paper, we adopt the idea of the Nevilleʹs algorithm to construct a kind of blending rational interpolants via continued fractions. For a given set of support points, there are many ways to build up the interpolation schemes, by which we mean that there are many choices to make to determine the initial interpolants on subsets of support points and then update them step by step to form a solution to the full interpolation problem. Numerical examples are given to show the advantage of our method and a multivariate analogy is also discussed.