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Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can…
This paper deals with Hermite osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with…
In this paper, we obtained some global approximation results for general Gamma type operators.
A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and…
Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with…
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that…
Recent work on dissimilarity-based hierarchical clustering has led to the introduction of global objective functions for this classical problem. Several standard approaches, such as average linkage, as well as some new heuristics have been…
Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
We obtain estimates in simultaneous approximation for a summation-integral type genuine hybrid operator. The convergence of derivatives of operator to the corresponding derivatives of the functions is proved and estimates for rate of…
We consider the approximation of manifold-valued functions by embedding the manifold into a higher dimensional space, applying a vector-valued approximation operator and projecting the resulting vector back to the manifold. It is well known…
We introduce an interpolation--regression operator for polynomial approximation on the unit sphere $\mathbb{S}^2$ from discrete samples. The approximant is a spherical polynomial of degree $r$ which interpolates the data on a prescribed…
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
We consider an approximation scheme for multivariate information assuming that synergistic information only appearing in higher order joint distributions is suppressed, which may hold in large classes of systems. Our approximation scheme…
In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of the uniform approximation for uniformly continuous and bounded functions/signals belonging to Lipschitz…
We design quasi-interpolation operators based on piecewise polynomial weight functions of degree less than or equal to $p$ that map into the space of continuous piecewise polynomials of degree less than or equal to $p+1$. We show that the…
Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…