单迭代法

In Chapter 2, we will use one-parameter subgroups of the Lie group to develop a version ofNewton\'s method on an arbitrary Lie group for maps from a Lie group to its correspondingLie algebra which is independent of affine connections on the Lie group and differs fromNewton\'s method for sections on Riemannian manifolds.

在第2章中，我们主要研究关于从李群到其李代数的映射f的Newton法的收敛性。利用李群的单参数子群来给出关于映射f的Newton迭代点列，此Newton迭代与李群上的联络无关，也与第1章中研究的Newton迭代不同。

The convergence of the traditional nonlinear equations is related to the selected initial value, but the convergence of the fixed point method is not related to it.

传统的非线性有限元方程组的数值求解法（牛顿-拉普森迭代法与共轭梯度法）只能求解单值性有限元方程，且其收敛行为与初始值的选择有关，而不动点方法在求解非线性方程组时的收敛行为不受初始值选择的影响，在大范围内是一致收敛的。

Study of capacity of single-core cable based on iterative method.

基于迭代法的单芯电缆载流量的研究。

In this thesis, the methods for solving eigenvalue problems and conventional reanalysis methods are studied firstly. Then, a new reanalysis method for real modal reanalysis of structures subjected to topological modification with added degrees of freedom is presented. This method is composed of the single step perturbation method and the Rayleigh-quotient iteration. The numerical examples show that this reanalysis method is very effective and high-quality.

本文首先在对常规的特征值数值求解方法和重分析方法研究的基础上，针对实模态的自由度增加的结构拓扑修改重分析，提出了一种新方法，该方法由于结合了单步摄动法和瑞利商逆迭代法两者的优点，应当是一种比较理想的重分析方法，算例的数值结果也有力的验证了该方法确实是一种高精度、十分有效的实模态重分析方法。

A four-point algorithm is presented in this paper for finding the least-squares solution of R and T,which is based on the singular value decomposition of matrix,and the derivation of the algorithm is provided too.

本文提供一种基于矩阵单值分解求解R和T的最小二乘解的四点算法，并对算法进行了推导，该算法与迭代法相比，具有速度快、用点少的优点，尤其适用于实际应用的颅脑手术可视化系统。

It is proved that Newton iteration method is still quadratically convergent under a weak condition, and a new point is added to Newton s method , i.

本文讨论求解非线性方程的牛顿法，证明牛顿法在一个弱条件下仍保持局部二阶收敛性，给出牛顿法的一点改进，即一个不带导数的单参数的二阶收敛的迭代法，而且分别得到这两种迭代法的收敛因子，最后进行数值实验

A warp skeleton method was proposed to solve the descriptive issue of arbit rary 3D woven composite architecture , with the unit cell being decomposed into subcells/ grids. The subcell vector concept was int roduced to digitalize the 3D architecture , in order to use the 2D database table to store it .

利用经纱脉络描述法解决了任意三维机织复合材料的结构表征问题；提出了单胞分解法与亚胞向量概念，实现了三维结构的二维化、数字化，根据数字表征结果和经典截面假设构造了初始断裂模型；使用一种迭代算法对初始断裂模型进行优化，使纱线束逐步逼近真实形态，进而实现三维实体造型，在此基础上进行网格剖分。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。