Bernstein-like polynomial approximation in higher dimensions
نویسندگان
چکیده
منابع مشابه
Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics
In this paper, we unify classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the method to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Appr...
متن کاملThe Trigonometric Polynomial Like Bernstein Polynomial
A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of r...
متن کاملEfficient Approximation Algorithms for Point-set Diameter in Higher Dimensions
We study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...
متن کاملThe generalized Bernstein problem on weighted Lacunary polynomial approximation
We obtain a necessary and sufficient condition for the lacunary polynomials to be dense in weighted Lp spaces of functions on the real line. This generalizes the solution to the classical Bernstein problem given by Izumi, Kawata and Hall. © 2005 Elsevier Inc. All rights reserved.
متن کاملOn Bernstein Type Inequalities for Complex Polynomial
In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.
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: Pacific Journal of Mathematics
سال: 1983
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1983.109.305