一种有理插值逼近的若干结果

设f(x)∈c[-1,1],α是大于零的实数。令Q_n^(α)[f,x]和_n^(α)[f,x]是两个正的有理插值算子。本文的主要结果是定理1 令f(x)∈c[-1,1],α>1是实数,则下面的不等式成立 (i)|Q_n^(α)[f,x]-f(x)|≤cω_f(1/n) (ii)|_n^(α)[f,x]-f(x)|≤cω_f(1/n) 定理2 令f(x)∈c[-1,1],α>3/2是实数,则下面的不等式成立 (i)|Q_n^(α)[f,x]-f(x)|≤cω_f((1-x^2)^(1/2)/n+1/n^2) (ii)|_n^(α)[f,x]-f(x)|≤cω_f((1-x^2)^(1/2)/n+1/n^2)

一种多元有理插值逼近

讨论多元有理插值逼近问题 ,且证明它们的逼近阶为ωf( 1n) ,其中ωf( 1n)表示连续模 ,n表示矩形区域剖分竖直线的数目 .

|x|^(α)(1≤α<2)在改进的正切节点组的有理逼近

本文研究了|x|α在改进的正切结点组的有理逼近的问题.利用改变结点的方法,获得其逼近阶为O(1/n^(4α))的结果.推广了一些学者在正切结点组下的研究的逼近阶,而且优于等距结点组、第一和第二类Chebyshev结点组的结果.

The Order of Approximation by Complex Rational Type Interpolating Operators at Fejer's Points

In this paper, supose Γ be a boundary of a Jordan domain D and Γ satisfied Альпер condition, the order that rational type interpolating operators at Fejer's points of f(z)∈C(Γ) converge to f(z) in the sense of uniformly convergence is obtained.

Some Remarks on Rational Interpolation to |x|

The present paper constructs a set of nodes which can generate a rationalinterpolating function to approximate |x|at the rate of O(1/(nk log n))for any givennatural number κ.More importantly.this construction reveals the fact that the higherdensity the distribution of a set of nodes has to zero (that is the singular point of thefunction |x|!),the better the rational interpolation approximation behaves.This probablyalso provides an idea to construct more valuable sets of nodes in the future.