This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through...

Abstract. We consider 3-monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we obtain Jackson-type estimates on the degree of 3-monotone approximation by piecewise polynomials ...

in this study, based on the optimal free derivative without memory methods proposed by cordero et al. [a. cordero, j.l. hueso, e. martinez, j.r. torregrosa, generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, mathematical and computer modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...

In this paper we use some well known theorems of algebraic geometry in reducing polynomial Hermite interpolation and approximation in any dimension to the solution of linear systems. We present a mix of symbolic and numerical algorithms for low degree curve ts through points in the plane, surface ts through points and curves in space, and in general, hypersuface ts through points, curves, surfa...

Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness cond...

Design optimization problems are often formulated as PDEconstrained optimization problems where the objective is a function of the output of a large-scale parametric dynamical system, obtained from the discretization of a PDE. To reduce its high computational cost, model order reduction techniques can be used. Two-sided Krylov-Padé type methods are very well suited since also the gradient to th...

This paper is concerned with non-stationary subdivision schemes. First, we derive new sufficient conditions for Cν smoothness of such schemes. Next, a new class of interpolatory 2m-point non-stationary subdivision schemes based on Gaussian interpolation is presented. These schemes are shown to be CL+μ with L ∈ Z+ and μ ∈ (0, 1), where L is the integer smoothness order of the known 2m-point Desl...

INTRODUCTION Few means exist to provide quantitative and reproducible assessment of vaginal conditions from biomechanical and functional standpoints. AIM To develop a new approach for quantitative biomechanical characterization of the vagina. METHODS Vaginal tactile imaging (VTI) allows biomechanical assessment of soft tissue and function along the entire length of the anterior, posterior, ...