Uniform convergence of derivatives of Lagrange interpolation
نویسندگان
چکیده
منابع مشابه
On Improvement of Uniform Convergence of Lagrange Interpolation Polynomials
Due to the Lagrange interpolation polynomials do not converge uniformly to arbitrary continuous functions, in this paper, a new interpolation polynomial is constructed by using the weighted average method to the interpolated functions. It is proved that the interpolation polynomial not only converges uniformly to arbitrary continuous functions, but also has the best approximation order and the ...
متن کاملConvergence of Extended Lagrange Interpolation
The authors give a procedure to construct extended interpolation formulae and prove some uniform convergence theorems.
متن کاملOn quadrature convergence of extended Lagrange interpolation
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...
متن کاملExtended Lagrange interpolation in weighted uniform norm
The author studies the uniform convergence of extended Lagrange interpolation processes based on the zeros of Generalized Laguerre polynomials. 2009 Elsevier Inc. All rights reserved.
متن کاملPointwise convergence of derivatives of Lagrange interpolation polynomials for exponential weights
For a general class of exponential weights on the line and on (−1, 1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near ±∞ (Freud weights), even weights of faster than smooth polynomial decay near ±∞ (Erdős weights) and even weights which vanish strongly near ±1, for example Pollaczek type weights. 1991...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1992
ISSN: 0377-0427
DOI: 10.1016/0377-0427(92)90258-y