If additional smoothness requirements and boundary conditions are met, the well–known approximation orders of scattered data interpolants by radial functions can roughly be doubled.

A proof of Favard can be restructured using quasi-interpolants of the type discussed in these proceedings [6] and his result strengthened.

Let a sufficiently smooth function f on [−1, 1] be sampled at n + 1 equispaced points, and let k ≥ 0 be given. An Euler–Maclaurin interpolant to the data is defined, consisting of a sum of a degree k algebraic polynomial and a degree n trigonometric polynomial, which deviates from f by O(n−k) and whose integral is equal to the order k Euler–Maclaurin approximation of the integral of f . This in...

In this article, we use the knowledge of positive definite tensors to develop a concept multi-kernels construct kernel-based interpolants scattered data. By techniques reproducing kernel Banach spaces, optimal recoveries and error analysis are shown for special class strictly multi-kernels.

Craig interpolation for satisfiability modulo theory formulas have come more into focus for applications of formal verification. In this paper we, introduce a method to reduce the size of linear constraints used in the description of already computed interpolant in the theory of linear arithmetic with respect to the number of linear constraints. We successfully improve interpolants by combining...

We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.

Abstract Uniform interpolants were largely studied in non-classical propositional logics since the nineties, and their connection to model completeness was pointed out literature. A successive parallel research line inside automated reasoning community investigated uniform quantifier-free (sometimes referred as “covers”) first-order theories. In this paper, we investigate cover transfer theory ...

Abstract In this paper, the solution to a bivariate Appell interpolation problem proposed in previous work is given. Bounds of truncation error are considered. Ten new interpolants for real, regular, functions constructed. Numerical examples and comparisons with Bernstein polynomials