Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...

Let X be a triangular array of interpolation points in a compact subset of [0; 2 ]. We obtain a necessary and su¢ cient condition for the existence of p > 0 such that the associated trigonometric polynomials are convergent in Lp. We also examine Lagrange interpolation on the unit circle. The results are analogues of our earlier ones for Lagrange interpolation on a real interval. 1. The Result I...

A classical approach to interpolation of sampled data is polynomial interpolation. However, from the sampling theorem it follows that the ideal approach to interpolation is to convolve the given samples with the sinc function. In this paper we study the properties of the sinc-approximating kernels that can be derived from the Lagrange central interpolation scheme. Both the finite-extent propert...

Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the applicabili...

In this paper is presented a parallel algorithm for computing a Lagrange interpolation on a Extended Fibonacci Cube EFC 1(n).The algorithm consists of three phases: initialisation phase, main phase in wich the Lagrange polynomials are computed and final phase in wich the terms of the interpolation formula are added together.

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...

This text discusses barycentric Lagrange interpolation based on the SIAM REVIEW article of Jean-Paul Berrut and Lloyd N. Trefethen [1]. It also offers additional background information, as well as some MATLAB demonstrations. Interpolation Given a set Dn of n + 1 nodes x j with corresponding values f j where j = 0, . . . ,n, we aim to construct the polynomial that satisfies p(x j) = f j j = 0, ....