Abstract Given gridded cell-average data of a smooth multivariate function, we present constructive explicit procedure for generating high-order global approximation the function. One contribution is derivation approximations to point-values function directly from data. The second development univariate B-spline-based quasi-interpolation operators using Multivariate spline are obtained by tenso...

Due to the Lagrange interpolation polynomials do not converge uniformly to arbitrary continuous functions, in this paper, a new interpolation polynomial is constructed by using the weighted average method to the interpolated functions. It is proved that the interpolation polynomial not only converges uniformly to arbitrary continuous functions, but also has the best approximation order and the ...

In this paper, we present a class of distributed approximating functionals ~DAF’s! for solving various problems in the sciences and engineering. Previous DAF’s were specifically constructed to avoid interpolation in order to achieve the ‘‘well-tempered’’ limit, in which the same order error is made both on and off the grid points. These DAF’s are constructed by combining the DAF concept with va...

In this contribution, we extend the polynomial-based ML approach derived earlier for synchronization purposes to the non-data-aided (NDA) case. We propose a fully digitally implemented synchronization concept using interpolation for jointly estimating the timing and phase. The interpolation methods used in this context can be implemented using the so-called Farrow structure. The ML function is ...

The Newton-Lagrange interpolation is a well-known problem in elementary calculus. Recall basic facts concerning this problem [6], [2]. Let Ak, k = 0, 1, 2, . . . and ak, k = 0, 1, 2, . . . be two arbitrary sequences of complex numbers (we assume that all ak are distinct ak 6= aj if k 6= j. By interpolation polynomial we mean a n-degree polynomial Pn(z) whose values at points a0, a1, . . . , an ...

It is well known that there exist continuous functions whose Lagrange interpolation polynomials taken at the roots of the Tchebycheff polynomials T„ (x) diverge everywhere in (-1, + 1) .' On the other hand a few years ago S . Bernstein proved the following result' : Let f(x) be any continuous function ; then to every c > 0 there exists a sequence of polynomials ~p„(x) where ~0 ,(x) is of degree...

Quadrature convergence of the extended Lagrange interpolant L2n+1f for any continuous function f is studied, where the interpolation nodes are the n zeros τi of an orthogonal polynomial of degree n and the n+ 1 zeros τ̂j of the corresponding “induced” orthogonal polynomial of degree n + 1. It is found that, unlike convergence in the mean, quadrature convergence does hold for all four Chebyshev w...

This report presents several approaches aimed at reducing the bias and uncertainty of the free energy difference estimates obtained using the thermodynamic integration simulation strategy. The central idea is to utilize interpolation schemes, rather than the often-used trapezoidal rule quadrature, to fit the thermodynamic integration data, and obtain a more accurate and precise estimate of the ...