Interpolant-based model checking is an approximate method for computing invariants of transition systems. The performance of the model checker is contingent on the approximation computed, which in turn depends on the logical strength of the interpolants. A good approximation is coarse enough to enable rapid convergence but strong enough to be contained within the weakest inductive invariant. We...

s of the talks Alexander Aptekarev, Keldysh Institut, Moscow (Russia) Title:” On a discrete entropy of ortogonal polynomials” Abstract: We shall discuss geometrical meaning of the discrete entropy of the eigenvector basis and particularly eigenvectors formed by orthogonal polynomials. The we present a nice new formula for the discrete entropy of Tchebyshev polynomials. It is joint work with J.S...

Abstract: This study proposes new C rational cubic spline interpolant of the form cubic/quadratic with three shape parameters to preserves the geometric properties of the given data sets. Sufficient conditions for the positivity and data constrained modeling of the rational interpolant are derived on one parameter while the remaining two parameters can further be utilized to change and modify t...

We study the Lebesgue constant of the rational interpolant of Berrut (cf. [1]) when the interpolation points are equally distributed. In the more general case of the rational interpolant of Floater and Hormann (cf. [6]), we show by several numerical results, that the behavior of the Lebesgue constant on equally distributed points is consistent with that of Berrut’s interpolant.

This paper considers the interpolation for multi-dimensional data using Voronoi diagrams. Sibson's interpolant is well-known as an interpolation method using Voronoi diagrams for discretely distributed data, and it is extended to continuously distributed data by Gross. On the other hand, the authors studied another interpolation method using Voronoi diagrams recently. This paper outlines the au...

The fractal interpolation functions defined by iterated function systems provide new methods of approximation and quantification of experimental data. The polynomial fractal functions can be considered as generalization of the piecewise polynomial interpolants. Assuming some hypotheses on the original function, a bound of the representation of the error for this kind of approximants is obtained...

A construction is given for a planar rational Pythagorean hodograph spiral which interpolates any two-point G Hermite data that a spiral can match. When the curvature at one of the points is zero, the construction gives the unique interpolant that is the involute of a rational Pythagorean hodograph curve of the form cubic over linear. Otherwise, the spiral comprises an involute of a Tschirnhaus...

The problem of computing Craig interpolants in SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of interest –including that of equality and uninterpreted functions (EUF), linear arithmetic over the rationals (LA(Q)), and some fragments of linear arithmetic over t...