We extend the classical Budan-Fourier theorem to Hermite-Birkhoff splines, that is splines whose knots are determined by a finite incidence matrix. This is then applied to problems of interpolation by Hermite-Birkhoff splines, where the nodes of interpolation are also determined by a finite incidence matrix. For specified knots and nodes in a finite interval, conditions are examined under which...

In this paper, we shall introduce and study a family of multivariate interpolating refinable function vectors with some prescribed interpolation property. Such interpolating refinable function vectors are of interest in approximation theory, sampling theorems, and wavelet analysis. In this paper, we characterize a multivariate interpolating refinable function vector in terms of its mask and ana...

The analysis of spatial data occurs in many disciplines and covers a wide variety activities. Available techniques for such analysis include spatial interpolation which is useful for tasks such as visualization and imputation. This paper proposes a novel approach to interpolation using space-filling curves. Two simple interpolation methods are described and their ability to interpolate is compa...

Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this point, several state-of-the-art theorem provers and SMT solvers include tailor-made decision procedures for ADTs, and version 2.6 of the SMT-LIB standard includ...

pendence between measurements at different locations. Methods currently in use include kriging, inverse-disSpatial interpolation methods are frequently used to characterize tance weighting, and thin-plate smoothing splines, and patterns in soil properties over various spatial scales provided that the data are abundant and spatially dependent. Establishing these one can use numerous approaches w...

Prediction error filters (PEFs) can be used to interpolate seismic data, in the time domain (Claerbout, 1992) or in the frequency domain (Spitz, 1991). The theory for PEFs assumes stationarity, so typically the data are considered a little bit at a time in patches, and assumed to be locally stationary within a patch. An alternative is to use nonstationary filters, which effectively sets the pat...

The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Björck and Pereyra algorithm for solving Vandermonde systems of equations (Cf. [1]). Very often this algorithm produces very accurate solution. The problem of determining the Newton coefficients is intimatel...

The classical theorems of Mittag-Leffler and Weierstrass show that when $$(\lambda _n)_{n \geqslant 1}$$ is a sequence distinct points in the open unit disk $$\mathbb {D}$$ , with no accumulation $$(w_n)_{n any complex numbers, there an analytic function $$\varphi $$ on for which (\lambda _n) = w_n$$ . A celebrated theorem Carleson [2] characterizes when, bounded this interpolating problem can ...