Baskakov算子加权逼近的收敛阶

本文讨论了Ｂａｓｋａｋｏｖ算子加Ｊａｃｏｂｉ权逼近的收敛性，首先指出了按通常的加权范数，Ｂａｓｋａｋｏｖ算子是无界的。然后引入一种新的范数，在此范数下Ｂａｓｋａｋｏｖ算子具有压缩性，最后借助于Ｋ－泛函，我们着重讨论了它的特征刻划问题。     

Grunwald插值多项式算子的逼近阶

设J_n~(α,β)(x)(α,β>-1)是在[-1,1]上以ρ(x)=(1-x)~α(1+x)~β为权函数的n阶Jacobi正交多项式。l_k~(n)(x)(K=1,2,…,n)是以J_n~(α,β)(x)的零点{x~(n)_1,x_2~(n),…,X_n~(n)}为基点的Lagrange插值基本多项式,对于f(x)∈C[-1,1],其Grunwald插值多项式算子是(见[1]第Ⅲ部分;[2]P.196)     

关于无穷维算子的有限维最佳逼近

A method of approaching to the infinite-dimensional linear operators by the finite-dimensional operators is discussed. It is shown that,for every infinite-dimensional operator A and every natural number n,there exists an n-dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n-dimensional optimal approximations to be unique is obtained.     

一种神经网络算子及其逼近阶估计

讨论了一种神经网络算子f_n(x)=sum from -n~2 to n~2 (f(k/n))/(n~α)b(n~(1-α)(x-k/n)),对f(x)的逼近误差|f_n(x)-f(x)|的上界在f(x)为连续和N阶连续可导两种情形下分别给出了该网络算子逼近的Jackson型估计.     

Banach空间中有限秩算子的逼近问题

利用Banach空间几何方法证得: Banach空间中有界线性算子成为紧线性算子的充分必要条件是这个算子可以被有限秩的有界齐性算子一致逼近. 由此可揭示Enflo反例的本质所在.     

Bernstein-Fan插值算子的逼近阶估计及其算法程序

本文研究了具有三角形波基函数的Bernstein-Fan值算子的收敛定理和逼近阶估计，并给出了它的算法程序。     

再生核空间扣的一类最佳逼近及其应用

在［１－２］中分别定义了具有再生核的Ｈｉｌｂｅｒｔ空间Ｗ＾１２［ａ，ｂ］和Ｗ，并给出再生核的解析式。本文讨论再生核空间中线性算子的一类最佳逼近，给出逼近算子的表达式及误差估计，作为特例得到类似于［１－４］中的插值的公公式，数值积分公式和数值原函数公式，但本文的公式计算更简便。     

Baskakov—Kantorovitch算子的Lp逼近

本文研究了Ｂａｃｋａｋｏｖ－Ｋａｎｔｏｒｏｖｉｔｃｈ算子在Ｌｐ空间的逼近。     

某些多元线性正算子的加权逼近

本文首先给出了在Ｌｐ逼近意义下某些线性正算子加Ｊａｃｏｂｉ权逼近时的特征定理，作为应用，我们给出了多元Ｂａｓｋａｋｏｖ型算子、多元Ｓｚａｓｚ－Ｍｉｒａｋｊａｎ型算子和多元Ｂｅｔａ算子加权逼近时的特征刻划．     

具有二维核空间的分支解的有限维逼近

其中X_h是X的有限维子空间。[1—6]中对(1)的正常解支、单重极限点附近的解支以及简单分支点附近的解支这三种不同情形,分别讨论了逼近问题(2)的解的性质以及和(1)的解之间的误差估计。特别指出了在简单分支点附近,(2)一般不存在分支点。在工程结构的稳定性和过层曲分析中以及结构的屈曲优化设计中,都会出现二重特征值     

用线性弱正算子逼近

用线性正算子的逼近理论飞速发展,但正性是一个较强的限制,孙永生,王仁宏等研究过减弱正性限制,作者研究用线性弱正算子逼近,推广Korovkin定理和Grundmann定理等等.     

On Measuring the Efficiency of Kernel Operators in L p (R d )

It is well known that it is possible to enhance the approximation properties of a kernel operator by increasing its support size. There is an obvious tradeoff between higher approximation order of a kernel and the complexity of algorithms that employ it. A question is then asked: how do we compare the efficiency of kernels with comparable support size? We follow Blu and Unser and choose as a measure of the efficiency of the kernels the first leading constant in a certain error expansion. We use time domain methods to treat the case of globally supported kernels in L _p (R ^d), 1≤p≤∞.

     

Approximation of Unbounded Functions by Linear Positive Operators

A unified class of linear positive operators has been defined. Using these operators some approximation estimates have been obtained for unbounded functions. For particular linear positive operators these results sharpen and improve the earlier estimates due to Fuhua Cheng (J. Approx. Theory, 1984) and Xiehua Sun (J. Approx. Theory, 1988).     

Approximation of Hypersingular Integral Operators With Cauchy Kernel

In the present article, the hypersingular integral operator with Cauchy kernel H is approximated by a sequence of operators of a special form, and it is proved that the approximating operators H_n strongly converge to the operator H and for an algebraic polynomial of degree not higher than n the operators H_n and H coincide. Therefore, the estimate established in this article yields more exact results in terms of the convergence rate than traditional methods. At the end we give the approximate solution of the hypersingular integral equation of the first kind.     

Asymptotic Approximation with a Sequence of Positive Linear Operators

The rate of pointwise convergence for a sequence of positive linear operators L_n approximating continuous functions on a finite interval is considered. The complete asymptotic expansion for the operators L_n as n tends to infinity is presented. It turns out that the central factorial numbers of first and second kind play an important role in the asymptotic expansion. The present work is an extension to that reported by Ivan and Raa.     

Algebras of Approximation Sequences: Finite Sections of Band-Dominated Operators

We develop the stability theory for the finite section method for general band-dominated operators on l^p spaces over Z^k. The main result says that this method is stable if and only if each member of a whole family of operators – the so-called limit operators of the method – is invertible and if the norms of these inverses are uniformly bounded.     

正线性算子对无穷区间上有界变差函数的点态逼近度

用ＢＶ［０，∞）表示在［０，∞）的每一有限子区间上为有界变差函数的函数构成的空间。用表示ＢＶ［０，∞）上的正线性算子，其中ｄｔＫｎ（ｘ，ｔ）是非负测度且，则有定理如果Ｌｎ（｜ｔ－ｘ｜β，ｘ）≤Ｃ（ｘ）／ｎｖ，，这里β＞０，ｖ≥１，Ｃ（ｘ）是一个与ｘ有关的常数，对ｆ∈ＢＶ［０，∞）和ｘ∈（０，∞）有这里作为应用，给出算子的逼近估计．     

一类多元Gauss-Weierstrass算子线性组合的逼近

本文主要讨论一类多元Gauss-Weierstrass算子的线性组合的逼近性质,建立了一致逼近下的正、逆定理,并给出了逼近阶的特征刻画.     

On Kantorovich Process of a Sequence of the Generalized Linear Positive Operators

We define the Kantorovich variant of the generalized linear positive operators introduced by Ibragimov and Gadjiev in 1970. We investigate direct approximation result for these operators on p-weighted integrable function spaces and also estimate their rate of convergence for absolutely continuous functions having a derivative coinciding a.e., with a function of bounded variation.     

一类Durrmeyer算子线性组合的加权逼近

本文主要给出了一类Ｂｅｒｎｓｔｅｉｎ－Ｄｕｒｒｍｅｙｅｒ算子的线性组合在Ｌｐ逼近意义下加Ｊａｃｏｂｉ权逼近时的特征刻划．