Near-Best Approximation by a de la Vallée Poussin-type Interpolatory Operator
نویسنده
چکیده
We give a very simply computable interpolatory process, wich approximates in near-best order on [-1,1] in some Jacobi-weighted space.
منابع مشابه
A numerical method for the generalized airfoil equation based on the de la Vallée Poussin interpolation
The authors consider the generalized airfoil equation in some weighted Hölder–Zygmund spaces with uniform norms. Using a projection method based on the de la Vallée Poussin interpolation, they find an approximate polynomial solution which converges to the original solution like the best uniform weighted polynomial approximation. The proposed numerical procedure leads to solve a tridiagonal line...
متن کاملGeneralized De La Vallée Poussin Operators for Jacobi Weights
Starting from a natural generalization of the trigonometric case, we construct a de la Vallée Poussin approximation process in the uniform and L norms. With respect to the classical approach we obtain the convergence for a wider class of Jacobi weights. Even if we only consider the Jacobi case, our construction is very general and can be extended to other classes of weights.
متن کاملInterpolatory and Orthonormal Trigonometric Wavelets
The aim of this paper is the detailed investigation of trigono-metric polynomial spaces as a tool for approximation and signal analysis. Sample spaces are generated by equidistant translates of certain de la Vall ee Poussin means. The diierent de la Vall ee Poussin means enable us to choose between better time-or frequency-localization. For nested sample spaces and corresponding wavelet spaces,...
متن کاملBounded quasi-interpolatory polynomial operators
We construct bounded polynomial operators, similar to the classical de la Valleé Poussin operators in Fourier series, which preserve polynomials of a certain degree, but are defined in terms of the values of the function rather than its Fourier coefficients. AMS classification: 41 A 10, 41 A 05
متن کاملTrigonometric Wavelets and the Uncertainty Principle
The time-frequency localization of trigonometric wavelets is discussed. A good measure is provided by a periodic version of the Heisenberg uncertainty principle. We consider multiresolution analyses generated by de la Vall ee Poussin means of the Dirichlet kernel. For the resulting interpolatory and orthonormal scaling functions and wavelets, the uncertainty product can be bounded from above by...
متن کامل