It is well known that analytic interpolation theory has found various applications in systems and control, e.g., H∞ control, covariance extension problem for spectral estimation, filtering and gain equalization. For the engineering point of views, it is desirable to synthesize interpolants with bounded degree, where the interpolants correspond to the transfer functions, representing devices of ...

It is well known that rational interpolation sometimes gives better approximations than polynomial interpolation, especially for large sequences of points, but it is difficult to control the occurrence of poles. In this paper we propose and study a family of barycentric rational interpolants that have no real poles and arbitrarily high approximation orders on any real interval, regardless of th...

We propose a simple generalization of Shephard’s interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A...

In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated universal models of this fragment and give a complete characterization of the up-sets of Kripke models of intuitionistic logic which can be defined by meet-implic...

We introduce the concept of a refinable set relative to a family of contractive mappings on a metric space, and demonstrate how such sets are useful to recursively construct interpolants which have a multiscale structure. The notion of a refinable set parallels that of a refinable function, which is the basis of wavelet construction. The interpolation points we recursively generate from a refin...

Recent research on Boolean satisfiability (SAT) reveals modern solvers’ inability to handle formulae in the abundance of parity (xor) constraints. Although xor-handling in SAT solving has attracted much attention, challenges remain to completely deduce xor-inferred implications and conflicts, to effectively reduce expensive overhead, and to directly generate compact interpolants. This paper int...

In this work, we consider interpolants for Nystrr om methods, i.e., second order initial value problems. We give a short introduction to the theory behind the discrete methods, and extend some of the work to continuous, explicit Nystrr om methods. Interpolants for continuous, explicit Runge-Kutta methods have been intensively studied by several authors, but there has not been much eeort devoted...