Recent results reveal that the family of barycentric rational interpolants introduced by Floater and Hormann is very well-suited for the approximation of functions as well as their derivatives, integrals and primitives. Especially in the case of equidistant interpolation nodes, these infinitely smooth interpolants offer a much better choice than their polynomial analogue. A natural and importan...

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al. that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhan...

The Hermite polynomials are simple, effective interpolants of discrete data. These interpolants can preserve local positivity, monotonicity, and convexity of the data if we restrict their derivatives to satisfy constraints at the data points. This paper describes the conditions that must be satisfied for cubic and quintic Hermite interpolants to preserve these properties when they exist in the ...

The convergence of (diagonal) sequences of rational interpolants to an analytic function is investigated. Problems connected with their definition are shortly discussed. Results about locally uniform convergence are reviewed. Then the convergence in capacity is studied in more detail. Here, a central place is taken by a theorem about the convergence in capacity of rational interpolants to funct...

The univariate error formulas for Pad6 approximants and rational interpolants, which are repeated in Section 2, are generalized to the multivariate case in Section 4. We deal with "general order" multivariate Pad~ approximants and rational interpolants, where the numerator and denominator polynomials as well as the equations expressing the approximation order, can be chosen by the user of these...

A general theory of quasi-interpolants based on trigonometric splines is developed which is analogous to the polynomial spline case. The aim is to construct quasi-interpolants which are local, easy to compute, and which apply to a wide class of functions. As examples, we give a detailed treatment including error bounds for two classes which are especially useful in practice.

A general theory of quasi-interpolants based on trigonometric splines is developed which is analogous to the polynomial spline case. The aim is to construct quasi-interpolants which are local, easy to compute, and which apply to a wide class of functions. As examples, we give a detailed treatment including error bounds for two classes which are especially useful in practice.