Abstract A generic technique for the construction of diversity of interpolatory subdivision schemes on the base of polynomial and discrete splines is presented in the paper. The devised schemes have rational symbols and infinite masks but they are competitive (regularity, speed of convergence, computational complexity) with the schemes that have finite masks. We prove exponential decay of basic...

A new class of subdivision schemes is presented. Each scheme in this class reproduces polynomials up to a certain degree. We find that these schemes extend and unify not only the well-known Deslauriers–Dubuc interpolatory scheme but the quadratic and cubic B-spline schemes. This paper analyze their convergence, smoothness and accuracy. It is proved that the proposed schemes provide at least the...

Let s ≥ 1 be an integer, φ : Rs → R be a compactly supported function, and S(φ) denote the linear span of {φ(· − k) : k ∈ Zs}. We consider the problem of approximating a continuous function f : Rs → R on compact subsets of Rs from the classes S(φ(h·)), h > 0, based on samples of the function at scattered sites in R s. We demonstrate how classical polynomial inequalities lead to the construction...

This paper introduces a new family of c'-continuous interpolatory variable-degree polynomial splines and investigates their interpolation and asymptotic properties as the segment degrees increase. The basic outcome of this investigation is an iterative algorithm for constructing C4 interpolants, which conform with the discrete convexity and torsion information contained in the associated polygo...

The aim of this paper is to carry out an improved analysis the convergence Nyström and degenerate kernel methods their superconvergent versions for numerical solution a class linear Fredholm integro-differential equations second kind. By using interpolatory projection at Gauss points onto space (discontinuous) piecewise polynomial functions degree ?r?1, we obtain order 2r methods, while, iterat...

We identify a new class of algebraic relations satisfied by the zeros orthogonal polynomials that are eigenfunctions linear differential operators order higher than two, known as Krall polynomials. Given an polynomial family , we relate pN with pm for each m ≤ N (the case = corresponding to involve only). These identities obtained finding exact expressions similarity transformation relates spec...

Purpose: This study aimed to relate the level of physical force applied to the arterial wall by atraumatic clamps to the degree of endothelial and wall damage. Methods: Sixteen sheep carotid and femoral arteries were each demarcated into four segments 1 cm apart (total 64 segments). Each segment was clamped for 15 min with a standard angled DeBakey vascular clamp. Four levels of force were gene...

Modification of Newtons method with higher-order convergence is presented.The modification of Newtons method is based on Frontinis three-order method The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...

The four-point interpolatory subdivision scheme of Dubuc and its generalizations to irregularly spaced data studied by Warren and by Daubechies, Guskov, and Sweldens are based on fitting cubic polynomials locally. In this paper we analyze the convergence of the scheme by viewing the limit function as the limit of piecewise cubic functions arising from the scheme. This allows us to recover the r...

This paper provides several constructions of compactly supported wavelets generated by interpolatory reenable functions. It was shown in D1] that there is no real compactly supported orthonormal symmetric dyadic reenable function, except the trivial case; and also shown in L] and GM] that there is no compactly supported interpolatory orthonormal dyadic reenable function. Hence, for the dyadic d...