As a kernel independent algorithm, multilevel Green’s function interpolation method (MLGFIM) [1] [2] has been developed for electromagnetic problems from low frequency to fullwave simulation. This method inherits the multilevel tree structure of multilevel fast multipole algorithm (MLFMA) and adopts the interpolation technique of pre-corrected fast Fourier transform (PFFT). Compare with other f...

In this article we investigate the minimal dimension of a subspace of C1(R2) needed to interpolate an arbitrary function and some of its prescribed partial derivatives at two arbitrary points. The subspace in question may depend on the derivatives, but not on the location of the points. Several results of this type are known for Lagrange interpolation. As far as I know, this is the first such s...

The aim of this paper is to continue our investigation of the Lebesgue function of weighted Lagrange interpolation by considering Erdős weights on R and weights on [ 1;1]. The main results give lower bounds for the Lebesgue function on large subsets of the relevant domains. 1991 Mathematics subject classification (Amer. Math. Soc.): 41A05, 41A10.

Quadratic models are of fundamental importance to the eeciency of many optimization algorithms when second derivatives of the objective function innuence the required values of the variables. They may be constructed by interpolation to function values for suitable choices of the interpolation points. We consider the Lagrange functions of this technique, because they have some highly useful prop...

In this paper we discussed issues related to resampling speech signal at arbitrary frequency by using interpolation methods. The implementation of four resampling methods, 1. direct interpolation, 2. Lagrange interpolation, 3. sine interpolation and, 4. Taylor series method, is presented. These methods have been tested with some speech data and various resampling frequencies. The quality of the...

A trivariate Lagrange interpolation method based on C cubic splines is described. The splines are defined over a special refinement of the Freudenthal partition of a cube partition. The interpolating splines are uniquely determined by data values, but no derivatives are needed. The interpolation method is local and stable, provides optimal order approximation, and has linear complexity.

;.Ja, b) = max Z A(x)1 if -I -a < b -1 . a~xs6 k=1 The quantity 1) called Lebesgue constant plays an important role in the theory of Lagrange interpolation ; as G . FABER [1] showed 1 (2) ~ n (l, 1) -c 1 log n for an arbitrary system of nodes (1). Moreover, S . BERNSTEIN [2] proved that (3) Acta Mathematica Academiae Scientiarum Hungaricae Tomus 32 (1-2), (1978), 191-195. ON THE INTEGRAL OF THE...

f(xj) = p(xj), j = 1, . . . , n. This is sometimes called Lagrange interpolation to distinguish it from Hermite interpolation, see below. For the basics, see Chapter 7 in Heath. As in Heath, we let Pn be the (function) space of polynomials of degree at most n. We let C([a, b]) denote the set of continuous functions on the interval [a, b]. Similarly, we let C([a, b]) be the n times continuously ...

The recently proposed domain-free discretization (DFD) method is based on the Lagrange interpolation and polynomial-based differential quadrature (PDQ) method. In this article, the radial basis function (RBF) approximation is used in the DFD method as the interpolation scheme for function approximation, and the RBF-DQ method is applied to derivative approximation. The new variant of DFD method ...

Let Aρ denote the set of functions analytic in |z| < ρ but not on |z| ρ 1 < ρ < ∞ . Walsh proved that the difference of the Lagrange polynomial interpolant of f z ∈ Aρ and the partial sum of the Taylor polynomial of f converges to zero on a larger set than the domain of definition of f . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and H...