求常微分方程周期解的同伦方法

As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.     

广义线性回归拟似然估计的强相合性

本文研究了广义线性模型g=μ(x'β0)+e中形如的拟似然方程,在一定的条件下证明了当n充分大时此方程以概率1有解βn,得到了βn的强相合性和收敛速度.     

一类优化问题的快速收敛算法

给出了一个用于解决 LC1线性约束优化问题的 BFGS-SQP算法 ,这个算法是用 Armijo线性原则来求步长的 .为推广 BFGS-SGP算法 ,本文采用 Wolfe线性搜索原则来替代该 BFGS-SQP算法的 Armijo原则 ,经过分析 ,同样得到了 BFGS-SGP算法的全局收敛性及超线性收敛性     

一致凸Banach空间非扩张映像具误差的Ishikawa迭代

研究一致凸 Banach空间中非扩张映像迭代序列的收敛问题 ,使用了基于 Ishikawa迭代的一种具误差的 Ishikawa迭代 ,证明了非扩张映像的具误差的 Ishikawa迭代收敛定理 .     

一类时滞非线性系统的采样迭代学习控制

本文针对一类时滞非线性系统提出一种采样迭代学习控制算法,严格证明了该算法的指数收敛性.当系统满足所给出的条件时,跟踪误差以指数速率收敛至一个与采样周期有关的误差范围内.     

不同分布ρ混合序列的强收敛速度

讨论了ρ混合序列的强收效性,获得了与独立情形几乎一致的结果,推广了著名的Marcinkiewicz-Zygmund强大数律.     

关于任意相依随机序列的完全收敛性(英文)

引入极限对数似然比的概念作为任意随机序列的联合分布与其边缘分布的差异的随机性度量,用概率密度比构造几乎处处收敛的上鞅,在适当的条件下,给出任意随机序列完全收敛的若干定理.     

Iterative Algorithm for Finding Approximate Solutions of a Class of Mixed Variational-like Inequalities

The purpose of this paper is to investigate the iterative algorithm for finding approximate solutionsof a class of mixed variational-like inequalities in a real Hilbert space,where the iterative algorithm is presentedby virtue of the auxiliary principle technique.On one hand,the existence of approximate solutions of this classof mixed variational-like inequalities is proven.On the other hand,it is shown that the approximate solutionsconverge strongly to the exact solution of this class of mixed variational-like inequalities.     

Convergence Domains of AOR Type Iterative Matrices for Solving Non-Hermitian Linear Systems

We discuss AOR type iterative methods for solving non-Hermitian linear systems based on Hermitian splitting and skew-Hermitian splitting. Convergence domains of iterative matrices are given and optimal parameters are investigated for skew-Hermitian splitting. Numerical examples are presented to compare the effectiveness of the iterative methods in different points in the domain. In addition, a model problem of three-dimensional convection-diffusion equation is used to illustrated the application of our results.     

Extended Global Convergence Framework for Unconstrained Optimization

An extension of the global convergence framework for unconstrained derivative-free optimization methods is presented. The extension makes it possible for the framework to include optimization methods with varying cardinality of the ordered direction set. Grid-based search methods are shown to be a special case of the more general extended global convergence framework. Furthermore,the required properties of the sequence of ordered direction sets listed in the definition of grid-based methods are relaxed and simplified by removing the requirement of structural equivalence.