CONVERGENCE OF (0,1,2,3) INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES

1. IntroductionThis note deals with convergence of (0,1,2,3) illterpolation on an arbitrary system of nodes.Fisrt we illtroduce some definitions and notations.LetGiven a fiXed even integer m, let Ajk 6 Pm.--1 (the set of polynomials of degree at most mn-- 1)satisfyThen the (0,1,...,m--1) Hermite--Fej6r type illterpolation for f 6 C[--1, 1] is defined byand the (0,1,...,m--1) Hernilte interpolation for f e Cd--'[--1, 1] is defined by(of. [6]). We also need a well known fact:where 11' 11 sta…     

一类非均匀分形插值函数的可微性

本文研究一类分形插值函数的可微性问题，通过构造一迭代函数系，利用迭代函数系的唯一吸引子。给出了一类分形插值函数。并获得了此类分形插值函数在[0，1]区间上几乎处处可微和在[0，1]区间上某一点不可微判定的充分条件，推广了文献[2]的结论。     

关于球面上的一种Hermite插值

本文旨在提出单位球面上的一种Hermite插值格式.为此,本文首先研究了沿球面同轴圆周组上的Hermite插值问题,给出了三种适定的插值泛函组.然后研究了球面上的Hermite插值问题,给出了球面上Hermite插值的一种叠加插值法,即添加圆周组法.进一步将二者结合,导出了一类球面上Hermite插值的适定插值泛函组.为了说明这类适定插值泛函组的构造方法,在本文最后还给出了构造球面上低次Hermite适定插值泛函组的一些具体例子和数值算例.     

矩形元上插值算子压缩性质及有限元迭代校正

本文研究了矩形上插值算子的性质,证明了一维及二维情形下插值算子具有压缩性,从而证明了矩形元上有限元迭代校正解收敛,并对几种不同类型的L型区域给出了数值例子,最后对三维及三维就以上情形作出了讨论。     

DIMENSION AND DIFFERENTIABILIIY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS

In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension.     

n维散乱数据带自然边界条件多元多项式样条插值

考虑n维散乱数据Hermit-Birkhoff型插值问题,在使给定的目标泛极小的条件下,构造了一种带自然边界条件的多元多项式样条函数插值方法.重点研究了插值问题解的特征,存在唯一性和构造方法,并讨论了收敛性及误差,最后给出了一些数值算例对方法进行验证.     

THE RECOVERY OF FUNCTIONS OF PALEY-WIENER CLASS FROM IRREGULAR SAMPLINGS

It is shown that a function f which is in the classical Paley-Wiener class, and its k-th derivative f(k) can be recovered in the metric Lq(R),2 < q ≤ ∞, from its values on irregularly distributed discrete sampling set {tj}j∈z as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {tj}j∈z is a real sequence such that {eifj(?)}j∈z constitutes a Riesz basis for L2([-π,π]).     

FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND

We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and possessing only a finite number of singularities or a product of such function with a highly oscillatory coefficient function. Contrast to wavelet-like approximations, ourapproximation matrix is not sparse. However, the approximation can be construced in O(n) operations and requires O(n) storage, where n is the number of quadrature points used in the discretization. Moreover, the matrix-vector multiplication cost is of order O(nlogn). Thus our scheme is well suitable for conjugate gradient type methods. Our numerical results indicate that the algorithm is very accurate and stable for high degree polynomial interpolation.     

高阶Hermite-Fejér型内插

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).     

基样条插值的极限性质

本文证明了当m→∞时‖s^(k)mf-f^(k)‖p→0（1＜p＜∞,k=0,1,2）的充要条件是f∈Bπ,p,其中Bπ,p＝Bπ∩Lp(R),Bπ表示指数π型的整函数在R上限制为有界函数所构成的集合,而Smf是在整数点对f 插值的唯一确定的m-1次基样条,进而得一了函数类Bπ,p的三个等价的特征刻划。     

Cayley-Bacharach定理在沿平面代数曲线插值问题中的应用

1 引 言 本文是讨论关于沿平面代数曲线的Lagrange插值问题,该问题与在二维实平面R~2上的二元Lagrange插值有关.设n为非负整数并且e_n=1/2(n+1)(n_2).P_n代表所有全     

THE ALGEBRAIC METHOD OF RATIONAL INTERPOLATION

This paper deals with rational interpolation. From algebraic viewpoint, we present an algebraic formulation of rational interpolation and discuss the existence of the interpolation function. Finally an algorithm for univariate case and an example are presented.     

有理插值问题存在性的一个判别准则

１引言我们知道,多项式Ｌａｇｒａｎｇｅ插值是适定的［１,２］,但有理插值函数却未必存在［８,３］．并且到目前为止,也没有类似于多项式Ｌａｇｒａｎｇｅ插值的能够揭示插值结构的显式插值公式．不过有理插值已有许多算法,比如Ｓｔｏｅｒ算法,Ｔｈｉｅｌｅ倒差商算法,Ｓａｌｚｅｒ算法以及Ｗｕｙｔａｃｋ算法等等,见［８,４,５,６］．本文为寻求尽可能接近显式的插值公式,进而揭示有理插值问题的内在结构,得到了有理插值函数存在的一个充要条件,同时也给出了有理插值函数的一种表现形式,参见［１１］．本文约定,所有矩阵…     

SOME RESEARCHES ON WEAK CONVERGENCE OF KERGIN INTERPOLATION

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.     

A CLASS OF NEW NONCONFORMING FINITE ELEMENTS

A class of new nine-parameter nonconforming finite elements with convergent prop-erties are constructed in terms of the approach of interpolation methods in this paper. All of those finite elements can be viewed as the generalization of Zienkiewicz's finite element by dis-lurbing its parameters.     

PARAMETER IDENTIFICATION PROBLEM OF THE FRACTAL INTERPOLATION FUNCTIONS

Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function. In this paper, we first present an example to explain a relationship between iteration procedure and fractal function. Then we discuss conditions that vertical scaling factors must obey in     

SUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULARELEMENT OF THE FINITE ELEMENTSUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULARELEMENT OF THE FINITE ELEMENT

1. IntroductionAlthough we bed proved the superconvergence of quadratic triangular elem6ntsbefore 1985, the superconvergence reseaxch of k(k 2 3)-degree triangulax elemeds Onlyhas a few advances, e.g.,.Lin, Yan and Zhou (see [15]) Prove that the three degreeHerlnite elements possess superconvergence and Walilbin (see [5-7]) obtains a roughresult by using a fine interinr estimation, that is, the placement fUnCtion or its gradestmay have weak superconvergence in the lOcal syUUnetric points,e…     

HAKOPIAN插值的弱收敛性

1　引　　言在 1 982年 ,Ｈａｋｏｐｉａｎ[1 ]提出了一种新的多元插值 这种插值是Ｋｅｒｇｉｎ插值的一种发展 ( [2 - 4 ]) 王和来 [5]在 1 984年给出了这种插值的余项估计 梁在 [6 ]的基础上于 86年给出了二元Ｈａｋｏｐｉａｎ插值的Ｌａｇｒａｎｇｅ型表达式并对定义于单位圆盘上足够光滑的插值函数给出了它的收敛速度估计 [7] 圆盘上的二元Ｈａｋｏｐｉａｎ插值的导数收敛性在 [8]中进行了讨论 最近 ,在 97年 ,梁和吕 [9]进一步研究了Ｈａｋｏｐｉａｎ插值的积分收敛性 我们在这篇文章中对Ｈａｋｏｐｉａｎ插值的弱收敛性进行了研…     

半线性椭圆问题Petrov-Galerkin逼近及亏量迭代

本文考虑了二阶半线性椭圆问题的Petrov-Galerkin逼近格式,用双二次多项式空间作为形函数空间,用双线性多项式空间作为试探函数空间,证明了此逼近格式与标准的二次有限元逼近格式有同样的收敛阶.并且根据插值算子的逼近性质,进一步证明了半线性有限元解的亏量迭代序列收敛到Petrov-Galerkin解.