We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are more general than those constituted by the n roots of complex unimodular numbers and the class of functions is different from the usually studied. Moreover, ...

The isogeometric analysis is increasingly used in various engineering problems. It is based on Non-Uniform Rational B-Splines (NURBS) basis function applied for the solution field approximation and the geometry description. One of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. The main contri...

This paper presents a novel approach to implement the interpolation function by means of Lagrange interpolators. The proposed architecture does not require high-frequency multipliers. With respect to conventional sinc filters of a comparable order, the response of Lagrange interpolators is better both in the passband and in the stopband, while the proposed implementation requires only a small i...

Abstract. The concept of Lagrange and Hermite interpolation polynomials can be generalized. The spectral basis of idempotents and nilpotents of a factor ring of polynomials provides a powerful framework for the expression of Lagrange and Hermite interpolation in 1, 2 and higher dimensional spaces. We give a new definition of quantum Lagrange and Hermite interpolation polynomials which works on ...

Lagrange interpolation is a classical method for approximating a continuous function by a polynomial that agrees with the function at a number of chosen points (the “nodes”). However, the accuracy of the approximation is greatly influenced by the location of these nodes. Now, a useful way to measure a given set of nodes to determine whether its Lagrange polynomials are likely to provide good ap...

Article history: Available online 4 September 2008

in a multi-secret sharing scheme, several secret values are distributed among a set of n participants.in 2000 chien et al.'s proposed a (t; n) multi-secret sharing scheme. many storages and publicvalues required in chien's scheme. motivated by these concerns, some new (t; n) multi-secret sharingschemes are proposed in this paper based on the lagrange interpolation formula for polynomials andcip...

We discuss Lagrange interpolation on two sets of nodes in two dimensions where the coordinates of the nodes are Chebyshev points having either the same or opposite parity. We use a formula of Xu for Lagrange polynomials to obtain a general interpolation theorem for bivariate polynomials at either set of Chebyshev nodes. An extra term must be added to the interpolation formula to handle all poly...