行为混合阵列加权和的收敛性

本文研究了行为混合阵列加权和的收敛性.利用混合序列的Rosenthal型最大值不等式,讨论了混合阵列加权和的L1收敛性,依概率收敛性,几乎处处收敛性,及完全收敛性之间的等价关系,推广了行独立随机变量阵列相应的结果.     

NOD随机变量序列加权和的矩完全收敛性

讨论了NOD随机变量序列加权和的矩完全收敛性,获得了NOD随机变量序列加权和的矩完全收敛性的充要条件.这些结论显示了矩完全收敛性和矩条件之间的等价关系,同时推广了Wu Qunying(2011)的结果.     

混合阵列的收敛性

该文引入了混合阵列的概念,讨论了混合阵列的完全收敛性与依概率收敛性.所得结果,推广了行独立随机变量阵列相应的结果.此外还得到了一般随机变量阵列的完全收敛性与依概率收敛性.     

行为(ρ)混合阵列加权和的收敛性

本文研究了行为(ρ)混合阵列加权和的收敛性.利用(ρ)混合序列的Rosenthal型最大值不等式,讨论了(ρ)混合阵列加权和的L1收敛性,依概率收敛性,几乎处处收敛性,及完全收敛性之间的等价关系,推广了行独立随机变量阵列相应的结果.     

混合序列部分和的若干收敛性质

本文研究了混合序列部分和的若干收敛性质.利用Serfling不等式推广情形,证明了一类随机变量序列部分和的一个收敛性结果,获得了混合序列部分和的收敛性,并进一步得到了混合序列加权和的强收敛性和完全收敛性,推广并改进了文[2]中有关结果.     

双障碍问题的多重网格法

本文研究双障碍问题的多重网格法,提出了两类算法,证明了其收敛性及对贴合分量的有限步收敛性,同时对其中一种算法的特款提出了一个 k无关收敛性定理。     

伪Newton—B族的导出及其性质

本文对无约束优化问题提出了一类新的近似牛顿法（伪牛顿-B族）,此方法同样具有二次终止性,产生的矩阵序列保持正定对称传递性。并证明了算法的全局收敛性和超级性收敛性。     

m步非线性多重分裂Newton法的收敛性

本文讨论了多重分裂算法在求解一类非线性方程组的全局收敛性和单侧收敛性．当用研步Newton法来代替求得每个非线性多重分裂子问题的近似解时，同样给出相应收敛性结论．数值算例证实了算法的有效性．     

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…     

ω-条件下Ulm-type方法的局部收敛性

由于牛顿法具有重要的理论基础和广泛的应用背景,它的收敛性得到了广泛研究([2,3,4,13,20,21,22,23]).—般而言,牛顿法的收敛性可以分成三类.一类是局部收敛性:已知方程(1)的解存在,初始点x0在该解的某个领域内时讨论牛顿法的收敛性([21,22,23]).     

Convergence of classes of subpramarts and games which become better with time

In this paper local convergence theorems for subpramarts and GBTs (games which become better with time) are presented. These results are also new for Martingales. Global convergence theorems for subpramarts and GBTs are also proved. These theorems are related to the theory of optimal stopping.     

赋范空间有界序列收敛的等价性

Two kinds of convergent sequences on the real vector space m of all bounded sequences in a real normed space X were discussed in this paper, and we prove that they are equivalent, which improved the results of [1].     

Lacunary equi-statistical convergence of positive linear operators

In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.      

On the Trotter-Kato theorem in a variable space

In this paper, the proof of a Trotter-Kato type theorem in a variable Banach space is given and some special cases and examples are considered.     

一类位置不变的Pickands型估计量

当极值指标大于0时, 本文提出了一种位置不变的Pickands型估计量,证明了该估计量的强弱相合性, 给出了其渐近展式和强收敛速度,并对$k_2$的最优选择进行了讨论,最后利用自适应性方法对该估计量和其它Pickands型估计量进行随机模拟分析,比较该估计量的优越性.     

Complete moment convergence for arrays of rowwise NSD random variables

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.     

关于不等式约束的信赖域算法

对于具有不等式约束的非线性优化问题，本文给出一个依赖域算法，由于算法中依赖区域约束采用向量的∞范数约束的形式，从而使子问题变二次规划，同时使算法变得更实用。在通常假设条件下，证明了算法的整体收敛性和超线性收敛性。     

THE CONVERGENCE OF BROYDEN ALGORITHMS FOR LC GRADIENT FUNCTION

1. IntroductionWe know that the variable metric algorithms, such as the Broyden algorithms, are veryefficient methods for solving the nonlinear programming problem:With exact line search, [11 proved that all the Broyden algorithms produce the same iterations for general functions. [21 proved that the rate of convergellce of these algorithms isone-step superlinear for the uniformly convex object function, and [3] proved that if thepoints given by these algorithms are convergent they are globall…     

i.i.d情况下非参数回归模型的误差密度估计的收敛性质

本文研究了i．i．d情况下非参数回归的误差密度估计的一致收敛和均方收敛，给出了一定条件下误差密度的估计量f^n(x)的一致收敛速度和均方收敛速度。