共查询到9条相似文献,搜索用时 15 毫秒
1.
THE DIVERGENCE OF LAGRANGE INTERPOLATION IN EQUIDISTANT NODES 总被引:1,自引:0,他引:1
LuZhikang XiaMao 《分析论及其应用》2003,19(2):160-165
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 this paper we show that the sequence of Lagrange interpolation polynomials corresponding to the functions which possess better smoothness on equidistant nodes in [- 1,1 ] still diverges every where in the interval except at zero and the end-points. 相似文献
2.
Len Bos 《Journal of Computational and Applied Mathematics》2011,236(4):504-510
It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes. 相似文献
3.
Hui Su Shusheng Xu 《分析论及其应用》2006,22(2):146-154
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
4.
In this paper we prove three conjectures of Revers on Lagrange interpolation for fλ(t)=|t|λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants LN( fλ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max|t|1| |t|λ−LN( fλ,t)|. The proofs are based on strong asymptotics for |t|λ−LN( fλ,t), 0|t|<1. 相似文献
5.
Summary Forn=1, 2, 3, ..., let
n
denote the Lebesgue constant for Lagrange interpolation based on the equidistant nodesx
k, n
=k, k=0, 1, 2, ...,n. In this paper an asymptotic expansion for log
n
is obtained, thereby improving a result of A. Schönhage. 相似文献
6.
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
7.
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
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.
Notes on orthogonal polynomials for exponential weights (Root-distances. Weighted Lebesgue function)
P. Vértesi 《Acta Mathematica Hungarica》2008,119(4):381-392
We prove some results on the root-distances and the weighted Lebesgue function corresponding to orthogonal polynomials for
exponential weights, where the weights are not necessarily symmetric.
Supported by the Hungarian National Science Foundation Grants (OTKA) T37299 and T047132. 相似文献