几类Kantorovich型插值算子在Orlicz空间内的逼近

分别讨论了以第二类Chebyshev多项式的零点、Jacobi多项式的零点、第一类Chebyshev多项式的零点为插值结点组的五类Kantorovich型插值算子在Orlicz空间内的逼近问题,得到了逼近阶的上界估计.     

修正的Grünwald插值算子在Orlicz空间内的加权逼近

本文研究了以第一类Chebyshev多项式的零点为插值结点组的一类修正的Grünwald插值算子在Orlicz空间内的加权逼近问题,运用Hardy-Littlewood极大函数,N函数的凸性,K-泛函,连续模以及Jensen不等式等工具,给出了这类插值算子在Orlicz空间内的逼近定理.     

推广的Grunwald插值在LBaM,ω空间中的逼近

本文研究了推广的Grunwald插值算子在LBaM,ω空间中的逼近.利用Orlicz空间范数和LBaM空间范数关系的不等式,以第一类Chebyshev多项式的零点为结点时,获得了两类推广的Grunwald插值算子在加权的LBaM,ω空间中的逼近阶.     

一种修正的拟Grünwald插值在Orlicz空间内的逼近度

修正了以第二类Chebyshev多项式的零点为插值结点组的拟Grünwald插值多项式,使之转化为积分形式,并利用不等式技巧和Hardy-Littlewood极大函数的方法,研究了此积分型拟Grünwald插值算子在带权Orlicz空间内的逼近问题,得出了意义相对广泛的逼近度估计的结果.     

一种修正的拟Grünwald插值在Orlicz空间内的逼近度

修正了以第二类Chebyshev多项式的零点为插值结点组的拟Grünwald插值多项式,使之转化为积分形式,并利用不等式技巧和Hardy-Littlewood极大函数的方法,研究了此积分型拟Grünwald插值算子在带权Orlicz空间内的逼近问题,得出了意义相对广泛的逼近度估计的结果.     

∣x∣在调整的第二类Chebyshev结点组的有理插值

本文研究了Newman型有理算子逼近|x|的收敛速度,插值结点组X取调整的第二类Chebyshev结点组.利用上界估计得到确切的逼近阶为O 1n2.这个结果优于结点组取作第一、二类Chebyshev结点组、等距结点组和正切结点组.     

推广的Grunwald插值在LM,ωBa空间中的逼近

本文研究了推广的Grunwald插值算子在L_M,ω^Ba空间中的逼近.利用Orlicz空间范数和L_M,ω^Ba空间范数关系的不等式,以第一类Chebyshev多项式的零点为结点时,获得了两类推广的Grunwald插值算子在加权的L_M,ω^Ba空间中的逼近阶.     

连续区间上积分值的MQ拟插值算子

在某些插值问题中,插值点处的函数值是未知的,而连续区间上的积分值是已知的.如何利用连续区间上积分值信息来解决函数重构是一个重要的问题.首先,文章利用连续区间上积分值的线性组合得到结点处函数值和一阶导数值的的四阶逼近.然后,构造了一类基于连续区间上积分值的MQ拟插值算子,它称之为积分值型MQ拟插值算子.最后,给出了该MQ拟插值算子的整体误差,它具有相应的四阶逼近阶.数值实验表明,该方法是有效可行的.     

2-周期整(m1,…,mp;m1′,…,mq′)插值的逼近性质

研究了一类等距结点上的2-周期整(m1,…,mp;m1′,…,mq′)插值算子的逼近性质,通过引入辅助算子得到了该插值算子在Lp(R)(1≤p＜∞)空间的饱和阶与饱和类.     

基于扰动结点的Lagrange插值算子逼近的 Steckin-Marchaud型不等式

建立了基于扰动超球Jacobi结点的Marcinkiewicz zygmund不等式并借助一种新的K泛函给出了基于扰动超球Jacobi结点的积分型Lagrange插值算子逼近的Steckin Marchaud型不等式.     

APPROXIMATION ORDER AND INTERPOLATION SPACES

In this paper we introduce the two-parameter operators on Abelian group and establish their interpolation theorems of approximation, which are extensions of the interpolation theorems for nonlinear best approximation by R. Devore and are suitable for the approximation of oprators.     

Fast one-sided approximation with spline functions

For the approximation of functions, interpolation compromises approximation error for computational convenience. For a bounded interpolation operator the Lebesque inequality bounds the factor by which the interpolation differs from the best approximation available in the range of the operator. A comparable process for one-sided approximation is not readily apparent. Methods are suggested for the computationally economical construction of one-sided spline approximation to large classes of functions, and criteria for comparing such approximation operators are investigated. Since the operators are generally nonlinear the Lebesque inequality is invalidated as an aid for comparing with the best one-sided approximation in the range of the operator, but comparable inequalities are shown to exist in some cases.     

Interpolation by neural network operators activated by ramp functions

In this paper, a family of interpolation neural network operators are introduced. Here, ramp functions as well as sigmoidal functions generated by central B-splines are considered as activation functions. The interpolation properties of these operators are proved, together with a uniform approximation theorem with order, for continuous functions defined on bounded intervals. The relations with the theory of neural networks and with the theory of the generalized sampling operators are discussed.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

W_2~m空间中样条插值算子与线性泛函的最佳逼近

In this paper,the convergency of spline interpolation operators is obtained,these spline operators are determined by linear differential operators and constraint functionals.The errors of the interpolating spline with EHB fanctionals are estimated.The best approximation of linear functionals on W2^n spaces are investigated,which let to a useful computational method for the approximation solution of higher order linear differential equations with multipoint boundary value conditions.     

Asymptotic Estimates for Interpolation and Constrained Approximation in H^{2} by Diagonalization of Toeplitz Operators

Sharp convergence rates are provided for interpolation and approximation schemes in the Hardy space that use band-limited data. By means of new explicit formulae for the spectral decomposition of certain Toeplitz operators, sharp estimates for Carleman and Krein-Nudel'man approximation schemes are derived. In addition, pointwise convergence results are obtained. An illustrative example based on experimental data from a hyperfrequency filter is provided. Submitted: August 17, 2001? Revised: November 5, 2001.     

Interpolation of several multiparametric approximation spaces

We prove a general interpolation theorem for linear operators acting simultaneously in several approximation spaces which are defined by multiparametric approximation families. As a consequence, we obtain interpolation results for finite families of Besov spaces of various types including those determined by a given set of mixed differences.     

拟Hermite-Fejr插值在一重积分Wiener空间下的平均误差

本文主要在Lp范数逼近意义下确定一类拟Hermite-Fejr插值多项式列在一重积分Wiener空间下平均误差的弱渐近阶.结果说明若概率空间不同,插值算子列在平均误差的意义下可能具有完全不同的逼近性质.在某些特殊情形下得到了其值或强渐近阶.     

Lagrange插值逼近导数的平均收敛

<正>We consider the rate of mean convergence of derivatives by Lagrange interpolation operators L_n(f,x) based on the zeros of Chebyshev polynomials of the first kind.A sharp estimate of the derivative of L_n(f,x)—f(x) in terms of the error of best approximation by polynomials of degree n is derived.     

Simultaneous Interpolation and Approximation by a Class of Multivariate Positive Operators

The purpose of this paper is to show that the interpolation positive operators of a wide class satisfy also the approximation property. Such a situation of simultaneous interpolation and approximation may be very desirable, but is rather unusual. Our attention is focused on the convergence problem, giving the conditions under which a sequence of operators of the considered class converges to a continuous function in a convex compact set in R ^m (m∈N). It must be recalled that many of these operators are very interesting in applications and that suitable algorithms can be devised for parallel, multistage and iterative computation.