收敛性

So in order to improve the convergence of Ritz vectors, firstly, refining -strategy is applied to the Davidson method in this paper. The process restarts with the refined Ritz vectors as the initial vectors, and then we get the refined block Davidson method. By analyzing the convergence of the new method, we give the theorem of it.

为了改善Ritz向量的收敛性，本文首先在块Davidson方法的执行过程中，运用精化策略，求出相应的精化向量并将其作为初始向量进行重新开始过程，由此得到了精化块Davidson方法，并对精化块Davidson方法进行了收敛性分析；其次，本文将精化块Davidson方法结合收缩技术，提出了收缩的精化块Davidson方法。

Since the concept of NA have a lot of applications in multivariate statistical analysis, reliability theory and percolation theory, various aspects of NA are significant and have been investigated by a host of scholars Fist, we give some Fuk-Nagaev type probability inequalities, moment inequalities of maximal partial sum for sequence of NA random variables, and some strong law of large numbers and complete convergence for sequence of NA random variables are obtained.

在本论文中我们对不要求强平稳或同分布的NA随机变量列进行了多方面的研究：首先对NA列建立了一组具有NA特点的关于最大部分和的Fuk-Nagaev型概率不等式及其关于某一类特定函数的矩不等式，它们在后续给出的极限定理的证明中发挥着重要作用；研究了具有不同分布的NA列的强收敛性，如对NA列建立了更一般条件下的Wittmann型强大数律及完全收敛性，同时也进一步改进了R。

Zero residual and non-zero residual problems are discussed in different parts in this paper and the algorithm is proven quadratic convergence for zero residual problems and superlinear convergence for non-zero residual problems.

新方法将问题划分为零残量和非零残量来讨论，并证明了算法对零残量问题具有二次收敛性，对非零残量问题具有超线性收敛性。

We estab-lish,under some mild assumptions,a locally quadratic convergence theoremfor Method I and prove a semi-local convergence theorem for Method II.Applications of the two methods to complementarity,variational inequalityand optimization problems are investigated as well.

在某些适当的假设下，我们证明了方法I的局部二次收敛性和方法II的半局部收敛性；还研究了两个方法在求解互补问题，变分不等式问题及约束优化问题中的应用。

It exploits the structured of the Hessian matrix of the objective function sufficiently. An attractive property of the structured BFGS method is its local superlinear/quadratic convergence property for the nonzero/zero residual problems.

它们充分利用了目标函数的Hesse矩阵的结构以提高算法的效率，该算法的显著优点是对于零残量问题具有二阶收敛性而对于非零残量问题具有超线性收敛性。

This paper presents a multigrid parallel algorithm of one dimensional virtual boundary ransack forecast, and discusses its convergence.

对网格方程组作多重网格区域分裂并行计算，虚拟边界预报提出一维搜索算法，并讨论相应的收敛性；通过 GS迭代的性质，构造区间压缩算法，证明了其收敛性。

According to disadvantage of AS that the speed low of convergentiss and easily entering the stagnation,improving the AS in some aspect by the way that importing pheromone windows that the value of pheromone cannot exceed the window,only deposit the pheromone on the edge that belongs to the iteration shortest solution path,releasing additional pheromone to the edge belongs to the so-far shortest solution path,judging the situation of convergent and to reinitialize pheromone,optimizing the solutions by local search procedure at the end of every iteration,modifying the transition probability by add some problem specific parameters and so on.

本文主要运用蚁群优化算法(Ant Colony Optimization，ACO)来求解VRP。针对蚁群算法收敛性比较差，易于停滞的缺陷，通过使用信息素窗口限制、信息素的最大最小值，只更新信息素迭代中最好解，增加了精英的蚂蚁，信息素重新初始化之前先判断出汇聚情况，在每次迭代过程中加入局部的搜索进行优化，在对蚁群算法进行了优化时考虑选择概率当中加入与问题的相关参数等措施，从而使蚁群算法的收敛性得到大大提高，避免了算法的停滞现象。

On this basis, according to historical data, apply ANN and differential simulation method to get the quantitatively correlative relations between each production and its own influence factors, and introduce the new methods of prediction for dynamic indexes with gas-field development (The combinatorial prediction method based on fuzzy comprehensive evaluation, the method of ANN to select optimally combinatorial prediction models and the ANN prediction method based on genetic algorithm).(2) Base on mathematical programming, combine with quantitative economics and techno-economics, introduce economical indexes to establish production"s distribution optimal model, production"s constitution optimal model and measured production"s constitution optimal model, including multi-objective models and five-years models. Upon this, the optimal project for all gas field and each gas-collected factory can be got. Also, introduce the time value of capitals to improve on these models.(3) Base on the optimal solution theory and algorithm theory for the nonlinear programming problem, introduce the SUMT algorithm and genetic algorithm to study how to solve the models, and on the basis of normal genetic algorithm, make use of auto-adaptively modulating method to improve on normal genetic algorithm; Base on algorithm"s convergence theory and calculation"s complexity theory to analyze seriatim SUMT algorithm"s convergence and genetic algorithms convergence, and compare performance with each other.

在此基础上，利用神经网络方法和微分模拟方法根据历史数据得到各分项产量与其影响因素之间的定量关联关系，并引入气田开发动态指标新的预测方法(基于模糊综合评判的组合预测方法、神经网络优选组合预测模型预测方法以及基于遗传优化的神经网络预测方法)；(2)以数学规划为基础，结合数量经济学和技术经济学，引入经济指标建立产量分配优化模型、产量构成优化模型、措施产量构成优化模型、气田开发多目标规划模型以及五年规划模型，进而获得全气田及各采气厂的最优方案，并引入资金时间价值对五年规划模型进行改进；(3)以非线性规划问题的最优解及算法理论为基础，引入SUMT算法以及遗传算法对模型的求解进行研究，并在原有的遗传算法基础上，引入自适应调整方法对遗传算法进行改进；以算法的收敛性理论和计算复杂性理论为基础，逐一分析SUMT算法以及遗传算法的收敛性，并比较三种算法的优劣性。

The inverted boundary data becomes closer to the exact solution when the number of elements increases, and numerical experiments show that the rate of convergence is higher for the formulation using the singular integral equation.

数值结果显示，当元素数目增加的时候，收敛性变得较佳；同时，使用奇异积分方程式的收敛性比较好。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。