A method of constructing a Chebyshev approximation multivariable functions by generalized polynomial with the exact reproduction its values at given points is proposed. It based on sequential construction mean-power approximations, taking into account interpolation condition. The calculated using an iterative scheme least squares variable weight function. An algorithm for calculating parameters...

The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vallée Poussin filters. In order to get an optimal in spaces of locally continuous functions equipped weighted uniform norms, the related Lebesgue constants have be uniformly bounded. previous works this has already been proved under different sufficient con...

Sparse interpolation refers to the exact recovery of a function as short linear combination basis functions from limited number evaluations. For multivariate functions, case monomial is well studied, now exponential functions. Beyond Chebyshev polynomial obtained tensor products univariate polynomials, theory root systems allows define variety generalized polynomials that have connections topic...

In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this topic. We also explore the relation between classical interpolation and sparse interpolation. We second consider the design of the interpolation points for th...

In the paper [8], the author introduced a set of Chebyshev-like points for polynomial interpolation (by a certain subspace of polynomials) in the square [−1, 1], and derived a compact form of the corresponding Lagrange interpolation formula. In [1] we gave an efficient implementation of the Xu interpolation formula and we studied numerically its Lebesgue constant, giving evidence that it grows ...

In this paper we perform a numerical study of Newton polynomial interpolation. We explore the Leja ordering of Chebyshev knots and the Fast Leja knots introduced by Reichel. In all previous publications we are aware of, the degree of interpolation polynomials in use is in the order of a few hundreds. We show that it is possible to employ degrees of up to one million or higher without a numerica...

A numerical approximation of the initial-boundary system of nonlinear hyperbolic equations based on spectral collocation method is presented in this article. A Chebyshev-Gauss-Radau collocation (C-GR-C) method in combination with the implicit RungeKutta scheme are employed to obtain highly accurate approximations to the mentioned problem. The collocation points are the Chebyshev interpolation n...