共查询到20条相似文献,搜索用时 0 毫秒
1.
Erich van Wickeren 《Constructive Approximation》1989,5(1):189-198
Equivalence theorems concerning the convergence of the Bernstein polynomialsB
n
f are well known for continuous functionsf in the sup-norm. The purpose of this paper is to extend these results for functionsf, Riemann integrable on [0, 1], We have therefore to consider the seminorm
相似文献
2.
It is well known that best complex rational Chebyshev approximants are not always unique and that, in general, they cannot be characterized by the necessary local Kolmogorov condition or by the sufficient global Kolmogorov condition. Recently, Ruttan (1985) proposed an interesting sufficient optimality criterion in terms of positive semidefiniteness of some Hermitian matrix. Moreover, he asserted that this condition is also necessary, and thus provides a characterization of best approximants, in a fundamental case.In this paper we complement Ruttan's sufficient optimality criterion by a uniqueness condition and we present a simple procedure for computing the set of best approximants in case of nonuniqueness. Then, by exhibiting an approximation problem on the unit disk, we point out that Ruttan's characterization in the fundamental case is not generally true. Finally, we produce several examples of best approximants on a real interval and on the unit circle which, among other things, give some answers to open questions raised in the literature. 相似文献
3.
In this paper, characterizations for lim
n(R
n
(f)/(n
–1)=0 inH
and for lim
n(n
r+
R
n
(f)=0 inW
r Lip ,r1, are given, while, forZ, a generalization to a related result of Newman is established.Communicated by Ronald A. DeVore. 相似文献
4.
We consider rational approximations of the form
|