S—λ导生的广义Feller算子对无界函数的逼近

由导源函数S（X）与扩充因子（X）导生的概率型逼近算子（简称PPA算子）是一类内容丰富的广义Feller算子，该文将概率方法与函数论方法相结合，解决了PPA算子对相当广泛的一类无界连续函数的逼近量化问题，并且还得出它们对无界不连续函数的逼近性态，体现了这类算子对无界数逼近的良好性能．结果包含了Khan「1」、Stancu「2］、Levikson［3］和XuJihua「4」的若干结果．     

关于苏联科学院数学研究所在函数逼近论方面的工作（上）

本文全面介绍了苏联科学院数学研究所的逼近论专家们多年来在函数逼近论的各个领域内所做的工作，这些领域包括：多项式的极值性质，一元周期函数与非周期函数逼近的正逆定理，线性逼近方法，多元函数逼近，函数类的宽度和求积公式等，在叙述这些成果的同时，作者还介绍了前人的有关结果．     

多项式加权一致逼近

了一个典型的ｎｏｎ－ｃａｒａｔｈｅｏｄｏｒｙ区域上的多项加权一致逼近结果，证明方法本身也给出了逼近的具体过程。     

广义黏性逼近方法及其应用

黏性逼近方法在非扩张映射不动点问题的研究中扮演着重要的角色。提出了一类广义黏性逼近方法，在一定条件下，证明了该算法的收敛性.作为应用，将所得的收敛性结果应用于求解约束凸优化问题与双层优化问题。     

椭圆最优控制问题分裂正定混合有限元方法的超收敛性分析

首先利用变分原理和最优化理论得到了原问题的等价最优性条件；其次构造了椭圆最优控制问题分裂正定混合有限元方法的逼近格式；再次通过引入一些重要的中间变量和投影算子，并利用投影算子的相关性质，结合分裂正定混合有限元本身的逼近结果，得到了椭圆最优控制问题分裂正定混合有限元方法的超收敛性；最后数值实验结果验证了所得理论结果的正确性.     

一类推广的Bernstein-Kantorovich算子的点态逼近

讨论Bernstein-Kantorovich算子的一种推广形式的逼近性质,运用插项的方法证明了逼近正定理,并证明了逆定理,得到了逼近等价定理.完善了算子在逼近性质方面的结果.     

极大熵方法与非单调曲线搜索可行方向法

1．引言逼近方法是解决复杂的最优问题的有效方法之一．目前，已有许多研究工作【‘一句．己有的工作主要是从理论上讨论逼近问题和原问题的最优解之间的关系．另一方面，寻求具体而有效的逼近方法不仅具有理论意义，而且更具有实用价值．近年来出现的求解非线性规划（minimaxfbi题）的极大滴方法I‘－‘］就是一种具体而有效的逼近方法．［1－3］中的有关结果可以用于这种方法．［7］则从另一途径给出了强凸规划的极大嫡方法的收敛性质．已有的极大滴方法的收敛性结果均是在最优解意义下得到的．由于一般情况下只能求得优化问题的Kuhn－T…     

C（[—π,π]^n）上多项式逼近的一些结果

首先给出C（[－π，π]n）上连续函数算子序列的一个逼近定理及其在多元多项式逼近方面的一个推论．其次，在所获结果的基础上，再利用高维乘积核构造非正的n维Rogosinski型核及相应的逼近算子，进而又得到了以二阶连续模为逼近阶的高维Rogosinski型逼近定理，     

关于Lax-Milgram定理和Cea定理的一个注记

本文研究抽象变分问题（不必要求具有强制性）的Galerhin方法，利用泛函分析理论证明了：若变分问题的Galerkin逼近问题存在唯一解，那么它本身的解存在唯一且可由Galerhin逼近解无限逼近的充要条件是其Galerkin逼近格式具有某种稳定性．此结果是对Lax-Milgram定理和Cea定理的补充，可以应用于不必具有强制性的变分问题．     

Couette-Taylor流的谱Galerkin逼近

利用谱方法对轴对称的旋转圆柱问的Couette—Taulor流进行数值模拟．首先给出Navier-Stokes方程流函数形式，利用Couette流把边界条件齐次化．其次给出Stokes算子的特征函数的解析表达式，证明其正交性，并对特征值进行估计．最后利用Stokes算子的特征函数作为逼近子空间的基函数，给出谱Galerkin逼近方程的表达式．证明了Navier-Stokes方程非奇异解的谱Galerkin逼近的存在性、唯一性和收敛性，给出了解谱Galerkin逼近的误差估计，并展示了数值计算结果。     

A-Statistical extension of the Korovkin type approximation theorem

In this paper, using the concept ofA-statistical convergence which is a regular (non-matrix) summability method, we obtain a general Korovkin type approximation theorem which concerns the problem of approximating a functionf by means of a sequenceL _n f of positive linear operators.     

On an Inverse Free Steffensen-Type Method for the Approximation of Stiff Differential Equations

In this article, an inverse free Steffensen-type method is introduced. The method is applied to approximate the systems of equations associated to implicit schemes approximating a stiff differential equation. The method has quadratic convergence without evaluating neither any derivative nor inverse operator. Finally, hypotheses ensuring the semilocal convergence and the R-order of convergence are presented.     

Local convergence of a secant type method for solving least squares problems

Local convergence of a secant type iterative method for approximating a solution of nonlinear least squares problems is investigated in this paper. The radius of convergence is determined as well as usable error estimates. Numerical examples are also provided.     

关于一种近似牛顿法的收敛性

§1.前言 设X和Y是Banach空间,p(x)是定义在区域G X上并取值于Y的非线性算子。假定p(x)有Frechet导算子p’(x),为了近似解算子方程 p(x)=0, (1)研究了如下的迭代程序: x_(n 1)=x_n-A_np(x_n), A_(n 1)=2A_n-A_np(x_(n 1)A_n,(2)这里x_0∈G和A_0∈(Y→X)都是初始近似,其中x_0是方程(1)的近似解,而A_0则是p(x_0)的近似过算子。[1]在一些条件下证明了程序(2)收敛于方程(1)的解。     

非扩张映射粘性逼近的强收敛性

在具有一致Gateaux可微范数的Banach空间中,研究了一个逼近非扩张映射不动点的粘性逼近方法,运用Banach极限推导了该逼近方法收敛的充分条件,并通过对该粘性逼近方法的修正逐步减少了收敛分析中的限制条件.     

Further investigation on iteration processes for pseudocontractive mappings with application

A new iterative method for approximating fixed points of bounded and continuous pseudocontractive mapping is proposed and a strong convergence theorem is obtained. As an application, we prove that a slight modification of our new scheme could be employed for approximating zeros of bounded and continuous accretive operators. Our theorems extend and unify most of the results that have been proved for this class of mappings.     

离散扰动下向量均衡问题的稳定性

利用集合序列P—K收敛的概念,讨论了离散扰动下的向量均衡问题弱有效解的稳定性．提出了一个新的向量均衡问题的极小化序列的概念．给出了各种充分条件以确保集合的包含关系,并举例阐述相应的结论．     

Numerical solution of stochastic differential equations by second order Runge–Kutta methods

In this paper we propose the numerical solutions of stochastic initial value problems via random Runge–Kutta methods of the second order and mean square convergence of these methods is proved. A random mean value theorem is required and established. The concept of mean square modulus of continuity is also introduced. Expectation and variance of the approximating process are computed. Numerical examples show that the approximate solutions have a good degree of accuracy.     

Extending the applicability of Newton’s method using nondiscrete induction

We extend the applicability of Newton’s method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Ptak. We obtain new sufficient convergence conditions for Newton’s method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F.A.Potra, V.Ptak, Sharp error bounds for Newton’s process, Numer. Math., 34 (1980), 63–72, and F.A.Potra, V.Ptak, Nondiscrete Induction and Iterative Processes, Research Notes in Mathematics, 103. Pitman Advanced Publishing Program, Boston, 1984. Under the same computational cost as before, we provide: weaker sufficient convergence conditions; tighter error estimates on the distances involved and more precise information on the location of the solution. Numerical examples are also provided in this study.     

On the asymptotic order of accuracy of Tikhonov regularization

In this paper, the rate of convergence and the order of accuracy (with respect to the error level in the data) of Tikhonov's method for approximating the minimal-norm least-square solution of an ill-posed operator equation is investigated. It is shown that, in general, this rate of convergence is arbitrarily small. It is further shown how this rate depends on some smoothness properties of the solution. All results describe optimal orders.