共查询到20条相似文献,搜索用时 15 毫秒
1.
The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang's main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm. 相似文献
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Yongping Feng+ 《计算数学(英文版)》2003,21(2):145-156
In this paper the uniform convergence of Hermite-Fejer interpolation and Griinwald type theorem of higher order on an arbitrary system of nodes are presented. 相似文献
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Biancamaria Della Vecchia Giuseppe Mastroianni Pter Vrtesi 《Journal of Computational and Applied Mathematics》1994,50(1-3):233-240
The authors consider a procedure of Hermite interpolation of higher order based on the zeros of Jacobi polynomials plus the endpoints ±1 and prove that such a procedure can always well approximate a function and its derivatives simultaneously in uniform norm. 相似文献
4.
本文讨论了n为奇数时πn(x)=(1-x2)P′n-1(x)零点上的(0,1,3)插值的正则性及收敛性,其中Pn-1表示n-1次Legendre多项式. 相似文献
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Ying-guang ShiDepartment of Mathematics Hunan Normal University Changsha China & Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2002,(2)
Abstract Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in theWeighted L~p norm on an arbitrary system of nodes are given. 相似文献
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The present paper investigates the convergence of Hermite interpolation operators on the real line. The main result is: Given 0 〈 δo 〈 1/2, 0 〈 εo 〈 1. Let f ∈ C(-∞,∞) satisfy |y|= O(e^(1/2-δo)xk^2,) and |f(x)|t= O(e^(1-εo )x2^). Then for any given point x ∈ R, we have limn→Hn,(f, x) = f(x). 相似文献
8.
The paper introduces Hermite-Fejr type (Hermite type) interpolation of higher order denoted by Smn(f)(S*mn(f)), and gives some basic properties including expression formulas, convergence relationship between Smn(f) and Hmn(f) (Hermite-Fejr interpolation of higher order), and the saturation of Smn(f). 相似文献
9.
史应光 《数学物理学报(B辑英文版)》2001,(1)
1 IntroductionThis paper deals with the uniform collvergence of truncated Hermte illterpolatioll oll anarbitrary systelll of 11odes. Tl1e mean collvergellce of trllllcated Herntite interpolation oll a11arbitrary syste12l of 1lodes 1las been st11died recently by tlle al1t11or[31. The converge11ce oftruncated Hern1ite illterpolatiou on tl1e zeros of the Jacobi polynontials is discussed in both tlleweigl1ted LP and the unfform norm by P. Vertesi and Y. X.[61.First we iutroduce some defi11itio… 相似文献
10.
Richard Baltensperger Jean-Paul Berrut Benjamin Noë l. 《Mathematics of Computation》1999,68(227):1109-1120
In 1988 the second author presented experimentally well-conditioned linear rational functions for global interpolation. We give here arrays of nodes for which one of these interpolants converges exponentially for analytic functions
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本文给出了以雅可比多项式的零点作为插值节点的一类插值多项式 Bn( f ;x)的导数逼近具有一阶连续导数的函数的收敛阶 .并且指出 limn→∞ Bn′( f;-1 )≠f′( -1 ) . 相似文献
13.
In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejér type interpolation in the
Lp norm on an arbitrary system of nodes are presented.
Project 19671082 supported by National Natural Science Foundation of China, I acknowledge endless help from Prof. Shi Ying-Guang
during finishing this paper. 相似文献
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Ying-guang Shi 《应用数学学报(英文版)》2002,18(2):277-288
Abstract
Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted L
p
norm on an arbitrary system of nodes are given.
Supported by the National Natural Sciences Foundation of China (No.19671082) 相似文献
17.
V. V. Novikov 《Mathematical Notes》2006,79(1-2):232-243
We obtain a uniform and sufficient condition for the convergence of the Lagrange interpolation process with Jacobi nodes on a closed interval [a, b] ? (?1, 1). The condition is stated in terms of the second differences of the interpolated function and uses its values only at the interpolation nodes. Some well-known criteria for uniform convergence are obtained as a consequence of our result. 相似文献
18.
Arnak Poghosyan 《分析论及其应用》2010,26(3):236-260
Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the jumps are approximated by solution of a system of linear equations. The accuracy of the jump approximation is explored and the corresponding asymptotic error of interpolation is derived. Numerical results validate theoretical estimates. 相似文献
19.
L. Szili 《Acta Mathematica Hungarica》2003,99(3):209-231
The aim of this paper is to investigate the summability of weighted Lagrange interpolation on the roots of Jacobi polynomials.
Starting from the Lagrange interpolation polynomials, we shall construct a wide class of discrete processes which are uniformly
convergent in a suitable weighted space of continuous functions. Error estimates for the approximation will also be considered.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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本文研究在单位圆周{|z| =1}上一致逼近函数f(z)及其导数,利用Hermite插值中的基函数建立复有理型插值,并证明它们在{|z| =1}上分别一致收敛于f(z)或f′(z) ,给出了收敛速度. 相似文献