This note shows that a wide class of algebraically motivated constructions for Lagrange interpolation polynomials always yields a tensor product interpolation space as long as the nodes form a tensor product grid or a lower subset thereof.

We determine the infinite sequences (ak) of integers that can be generated by polynomials with integral coefficients, in the sense that for each finite initial segment of length n there is an integral polynomial fn(x) of degree < n such that ak = fn(k) for k = 0, 1, . . . , n − 1. Let P be the set of such sequences and Π the additive group of all infinite sequences of integers. Then P is a subg...

Well-known two-sided estimates for the Lebesgue constants of two classical trigonometric interpolation Lagrange polynomials are improved. Approximations these based on logarithmic functions with shifted arguments.

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...

Several recent articles [l]-[3] have discussed the use ofLagrange polynomials for band-limited signal estimation. We find errorbounds when using Lagrange polynomials for interpolation and extra-polation of finite-power band-limited signals if a finite number of regularlyspaced noisy samples are used. I. INTR~DUC~ONSuppose f(t) has a (2N + 1)st derivative and the samplesf...

A set T ⊂ R at which interpolation from Π≤n(R ) (polynomials of degree ≤ n) is uniquely possible is a GCn-set if the associated Lagrange fundamental polynomials have only linear factors. For such GCn-sets T in the plane, Gasca and Maeztu conjectured the existence of a line containing n + 1 points from T. It is shown here that, already in R, there exist GC2-sets T without any hyperplanes contain...

In this paper, we derive an explicit formula for the bivariate Lagrange basis polynomials of a general set checkerboard nodes. This generalizes existing results at Padua nodes, Chebyshev Morrow-Patterson and Geronimus We also construct subspace spanned by linearly independent vanishing that vanish nodes prove uniqueness in quotient space defined as with certain degree over polynomials.

Abstract Stenger conjectures are claims about the location of eigenvalues matrices whose elements certain integrals involving basic Lagrange interpolating polynomials supported on zeros orthogonal polynomials. In this paper, we show validity extended conjecture for families classical We also restricted Strenger a family Jacobi and generalized Laguerre A connection with -stability collocation Ru...

We propose a new space efficient operator to multiply elements lying in a binary field F2k . Our approach is based on a novel system of representation called Double Polynomial System which set elements as a bivariate polynomials over F2. Thanks to this system of representation, we are able to use a Lagrange representation of the polynomials and then get a logarithmic time multiplier with a spac...

Given an odd prime p, we provide formulas for the Hensel lifts of polynomial roots modulo p, and give an explicit factorization over the ring of formal power series with integer coe cients for certain reducible polynomials whose constant term is of the form pw with w > 1. All of our formulas are given in terms of partial Bell polynomials and rely on the inversion formula of Lagrange.