All-digital approaches for the adjustment of timing offset in digital modems have attracted increasing attention. We recently announced a novel interpolation method which, instead of approximating the continuous-time signal with a conventional polynomial and computing the synchronized samples using a Farrow structure, uses a trigonometric polynomial. Simulation results indicate that improved pe...

In this paper we propose a new kind of Hermite interpolation on arbitrary domains, matching derivative data of arbitrary order on the boundary. The basic idea stems from an interpretation of mean value interpolation as the pointwise minimization of a radial energy function involving first derivatives of linear polynomials. We generalize this and minimize over derivatives of polynomials of arbit...

Title: Padé–type rational and barycentric interpolation. Abstract: In this paper, we consider the particular case of the general rational Hermite interpolation problem where only the value of the function is interpolated at some points, and where the function and its first derivatives agree at the origin. Thus, the interpolants constructed in this way possess a Padé–type property at 0. Numerica...

We associate a CNF-formula to every instance of the mean-payoff game problem in such a way that if the value of the game is non-negative the formula is satisfiable, and if the value of the game is negative the formula has a polynomial-size refutation in Σ2-Frege (i.e. DNF-resolution). This reduces mean-payoff games to the weak automatizability of Σ2-Frege, and to the interpolation problem for Σ...

The problem of modeling and visualization of scattered data where there are inherent constraints on value of the data exists in many scientific and business research areas. For example, the value of mass concentration always has the lower bound of 0 and upper bound of 1. The modeling functions having gradient continuity usually do not guarantee to preserve the bounds of data. In this paper we p...

This article considers the extension of V. A. Markov’s theorem for polynomial derivatives to polynomials with unit bound on the closed unit ball of any real normed linear space. We show that this extension is equivalent to an inequality for certain directional derivatives of polynomials in two variables that have unit bound on the Chebyshev nodes. We obtain a sharpening of the Markov inequality...

In this paper, we prove new embedding results by means of subspace interpolation theory and apply them to establishing regularity estimates for the biharmonic Dirichlet problem, and for the Stokes and the Navier-Stokes systems on polygonal domains. The main result of the paper gives a stability estimate for the biharmonic problem at the threshold index of smoothness. The classical regularity es...

A statistical way to describe a surface in space is by specifying the expected value and variance at each point, and their mutual covariances. The surface is assumed to consist of a trend function and a residual function. The covariances between those points are expressed in a covariance function, based on the residual function. An application of the covariance function is Kriging, an interpola...

In this paper, we provide an integral error formula for a certain scale of mean value interpolations which includes the multivariate polynomial interpolation schemes of Kergin and Hakopian. This formula involves only derivatives of order one higher than the degree of the interpolating polynomial space, and from it we can obtain sharp L1-estimates. These L1-estimates are precisely those that num...

The polynomial interpolation in one dimensional space R is an important method to approximate the functions. The Lagrange and Newton methods are two well known types of interpolations. In this work, we describe the semi inherited interpolation for approximating the values of a function. In this case, the interpolation matrix has the semi inherited LU factorization.