收敛的阶

Order Hilbert ill-conditioned linear equations were solved, and the relative error was less than 0.45%. Numerical experiments verified that the method was efficient compared with the efficient methods used commonly nowadays. Numerical experiments results showed that the conjugate vector base method was suited for solving large-scale ill-conditioned linear equations with fast convergence and high precision.

通过对5000阶的Hilbert方程组进行求解，结果的相对误差小于0.45%，并与当前普遍使用有效的方法进行了比较，数值实验结果表明，该算法适合求解大型病态线性方程组，且具有快速收敛，精度较高的特性。

By weakening the premise of the convexity of the objective function required in paper[7], we prove the sufficient desent property and the global convergence with the strong Wolfe line search.

在第二章中，我们参照文献[7]中的方法，提出了一类与HS算法相关的共轭梯度算法，并减弱了文[7]中要求目标函数二阶连续可微且为凸的前提条件，采用强Wolfe线搜索，在较弱的条件下证明了这一类算法具有充分下降性和全局收敛性。

The M Q algorithm has been applied to the second order elliptic problems with the Dirichlet boundary conditions,and the so called R condition is involved in the convergence theorem and the optimal relaxation parameter.

M-Q算法所考虑的是二阶椭圆型Dirichlet边值问题，此时有所谓的R条件成立，算法的收敛定理以及松弛因子的选取都需要该条件。

Many authors have studied the properties of the Edgeworth expansions for the distributions of Ustatistics since the invention.

关于标准化和学生化U统计量的分布，二阶展开的收敛速度问题成为了研究的核心内容，相关的研究成果已经非常丰富。

The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm.

利用矩阵理论证明了差分解的存在惟一性，并利用一个重要的不等式在先验估计的基础上，运用能量估计的方法证明了该格式按无穷范数以二阶精度收敛到真实解。

In Chapter 3, we study the semilocal convergence for the method appeared in Chapter 2 under Lipschitz continuous condition of the second Frechet derivative, and get the corresponding error estimation by majoriz-ing function technique. And also, an application of the theorem to a non- linear equation is given.

在第三章中，研究了复合型Newton-Steffensen迭代方法在算子的二阶导数满足Lipschitz连续条件时的半局部收敛性，并利用优函数技巧得到了其在该条件下的误差估计，最后给出了这个定理的一个应用。

Further, according to the positity of the Hessian matrix, which is got from the second order adjoint model, the uniqueness of the assimilation result is manifest. And the relationship between the rate of convergence and the frequency of the observation utilization in the assimilation is investigated.

进一步，借助二阶伴随模式所得到的Hessian矩阵，说明同化解是唯一的，并分析了优化算法的收敛速度与同化过程中观测资料使用频率的关系。

For improving convergence, this paper firstly introduces Lagrange function to solve constraint problem in large-scale system optimization, secondly constructs the hierarchical optimization networks for large-scale industrial systems with Hopfield network.

为了 提高算法的收敛速度，引入Lagrange函数解决大系统优化问题中的各种约束，并用Hopfield 网络实现了大系统稳态递阶优化的网络算法，最后给出了某一大系统辨识及优化的仿真结果。

Linear triangular element is considered to solve the second order elliptic boundary value problem in 2-D. By using of the distinctive structure and some novel approaches, we obtain the super-close and superconvergence results on certain kind of anisotropic meshes.

讨论在有限制的各向异性网格下用线性三角形有限元逼近二阶椭圆边值问题，利用单元构造的特殊性和一些新的技巧得到相应的超逼近和超收敛结果。

In the present work, usingFCPC method, we have performed systematically the theoretical investigationsfor the electronic charge density, high-order Zeeman effect and hyperfinestructure.

本文通过研究这些物理量的收敛性质发现，波函数第二项对这些物理量的合理描述起着重要的作用，特别是对高阶Zeeman效应和超精细结构参数的影响。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。