首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到17条相似文献,搜索用时 93 毫秒
1.
It is a classical result of Bernstein that the sequence of Lagrange interpolation polumomials to |x| at equally spaced nodes in [-1, 1] diverges everywhere, except at zero and the end-points. In the present paper, toe prove that the sequence of Lagrange interpolation polynomials corresponding to |x|^α (2 〈 α 〈 4) on equidistant nodes in [-1, 1] diverges everywhere, except at zero and the end-points.  相似文献   

2.
This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the rune tion f(z) =|x|^α(1〈α〈2) on [-1,1] can diverge everywhere in the interval except at zero and the end-points.  相似文献   

3.
This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the function f(x) =|x|~a(1相似文献   

4.
This paper investigates the optimal Hermite interpolation of a class F_(∞) of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,w)[-1,1],1≤p∞[-1,1]and L_(p,w)[-1,1],1≤p<∞ with w a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation polynomials based on the ze-ros of polynomials with the leading cofficient 1 of the least deviation from zero in L_(∞)[-1,1]and L_(p,w)[-1,1],1≤p<∞are optimal for 1≤p≤∞.We also give the optimal Hermite interpolation nodes when we ask the endpoints to be included in the nodes.  相似文献   

5.
S.M.Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant nodes in [-1,1]. In 2000, M. Rever generalized S.M.Lozinskii's result to |x|α(0 <≤ α≤ 1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|α1(1 < α < 2)..  相似文献   

6.
This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L[-1,1] and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoin...  相似文献   

7.
In this paper we present a generalized quantitative version of a result the exact convergence rate at zero of Lagrange interpolation polynomial to spaced nodes in [-1,1] due to M.Revers concerning f(x) = |x|α with on equally  相似文献   

8.
S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant nodes in [-1, 1]. In 2000, M. Rever generalized S.M. Lozinskii's result to |x|α(0 ≤α≤ 1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|α(1 <α< 2)..  相似文献   

9.
Recently Brutman and Passow considered Newman-type rational interpolation to |x| induced by arbitrary sets of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods,one could establish the exact order of approximation for some special nodes.In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval [0,1] and then extending this set to [-1,1] in a symmetric way.We show that in this case the exact order of approximation is O( 1 n 2 ).  相似文献   

10.
Recently Brutman and Passow considered Newman-type rational interpolation to |x| induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O(1/n|nn)  相似文献   

11.
It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to |x| at equally spaced nodes in [-1, 1] diverges everywhere, except at zero and the end-points. In the present paper, we prove that the sequence of Lagrange interpolation polynomials corresponding to |x|α(2 <α< 4) on equidistant nodes in [-1,1] diverges everywhere, except at zero and the end-points.  相似文献   

12.
In 1918 S. N. Bernstein published the surprising result that the sequence of Lagrange interpolation polynomials to |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In the present paper, we prove that the sequence of Lagrange interpolation polynomials corresponding to |x|α (0<α1) on equidistant nodes in [−1, 1] diverges everywhere in the interval except at zero and the end-points.  相似文献   

13.
This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the function f(x) = |x|α(1 <α< 2) on [-1, 1] can diverge everywhere in the interval except at zero and the end-points.  相似文献   

14.
本文研究\,$[-1,1]$上的一个无限可微函数类$F_\infty$在空间$L_\infty[-1,1]$及加权空间$L_{p,\omega}[-1,1]$, $1\le p< \infty$ ($\omega$是$(-1,1)$上的非负连续可积函数)的最优Lagrange插值.我们证明了基于首项系数为1且于$L_{p,\omega}[-1,1]$上有最小范数的多项式零点的Lagrange插值对$1\le p< \infty$是最优的. 同时我们给出了当结点组包含端点时的最优结点组.  相似文献   

15.
In this paper we present a generalized quantitative version of a result due to D. L. Berman concerning the exact convergence rate at zero of Lagrange interpolation polynomials to | x| a\left | x\right | ^{\alpha } based on equally spaced nodes in [-1, 1]. The estimates obtained turn out to be best possible.  相似文献   

16.
We show that for a broad class of interpolatory matrices on [-1,1] the sequence of polynomials induced by Hermite—Fejér interpolation to f(z)=z diverges everywhere in the complex plane outside the interval of interpolation [-1,1] . This result is in striking contrast to the behavior of the Lagrange interpolating polynomials. June 15, 1998. Date accepted: January 26, 1999.  相似文献   

17.
在构造拉格朗日插值算法时,插值结点的选择是十分重要的.给定一个足够光滑的函数,如果结点选择的不好,当插值结点个数趋于无穷时,插值函数不收敛于函数本身.例如龙格现象:对于龙格函数f(x)=1/1+25x^2,如果拉格朗日插值的结点取[-1,1]上的等距结点,那么逼近的误差会随着结点个数增多而趋于无穷大⑴,由此可知插值结点的选择尤为重要.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号