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。

Assignment Method Required Attributes Required Settings All or Nothing Time none Capacity Restraint Time Iterations Capacity Convergence Alpha Beta Incremental Time Iterations Capacity Convergence Alpha Beta User Equilibrium Time Iterations Capacity Convergence Alpha Beta Stochastic User Equilibrium Time Iterations Capacity Convergence Alpha Beta Function Error System Optimum Time Iterations Capacity Convergence Alpha Beta

表格格式乱了，就这么翻吧） 1。全有全无分配法。所需属性：时间；所需设置：无； 2。容量限制法。所需属性：时间，通行能力；所需设置：迭代，收敛，α，β； 3。增量分配法。所需属性：时间，通行能力；所需设置：迭代，收敛，α，β； 4。用户平衡法。所需属性：时间，通行能力；所需设置：迭代，收敛，α，β； 5。随机用户平衡法。所需属性：时间，通行能力；所需设置：迭代，收敛，α，β，函数，误差； 6。系统最佳法。所需属性：时间，通行能力；所需设置：迭代，收敛，α，β。

The numerical ex-periment has shown that the number of iterations depends significantly on the positiveparameterα,β. But, in general, it is di?cult to choose a proper parameterα,β. Thuswe propose new self-adaptive alternating direction method which adjusts the scale pa-rameter automatically per iteration based on the message of the iterates. We have provedthe convergence of the method under mild assumptions.Finally, we present some numerical results.

对于我们提出的新交替方向法，数值实验表明，迭代的步数与时间与所取的参数α，β有关，然而我们很难去选择一个合适的参数α，β，因此我们提出新自适应交替方向法，对其中的参数α，β进行自适应调整，这种自适应算法根据每步迭代信息自动地调整参数α，β，并证明了算法的收敛性。

The numerical results also indicate that the weighted geometric mean method needs less number of iteration than the weighted arithmetic mean method.

数值结果也显示：加权几何平均法所需的迭代次数比加权算术平均法所需迭代次数少。

Compared with the Ritz vector method,the scheme still keeps the feature of using sidgle vector for inverse iteration.

一般的Ri权向址法和助n二哪法都是从一个初始向量开始迭代，用带，卜交化的反迭代脚戈一组Ritz挂向叭和相应r内只对角矩阵，仅用一次R叮leigh一Ri垅分析法，求得若千最低阶特征解。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的"半收敛"性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

Charge example in whom five node form, 4 node adopt Newton - pressgang modest law go on trend calculate, another node to contain wind-driven generator adopt PQ change, take the place of model go on trend calculate, change, take the place of with ordinary trend computing method first, judge revision wind electrical machinery nodal voltage error go on for the second time changing and taking the place of in establishing range.

在五个节点构成的算例中，4个节点采用牛顿-拉夫逊法进行潮流计算，另外一个含有风力发电机的节点采用PQ迭代模型进行潮流计算，先用普通潮流计算法迭代，后经过修正风电机节点电压判定误差是否在设定范围内进行第二次迭代。

The original PageRank algorithm uses the Power Method to compute successive iterations that converge to the principal eigenvector of the Markov matrix representing the Web link graph.Authors use the sparse of the Google matrix P in the iterative matrix A =[ CP +（1- c ） E ]T,optimize the computation of each iteration and reduce storage space.

在PageRank算法中是使用乘幂法对网络链接图的Markov矩阵进行迭代计算，利用迭代矩阵 A =[ CP +（1- c ） E ]T中Google矩阵 P 的稀疏性，优化每次迭代的计算量并且减少空间存储量。

Some efforts were made to improve the computational efficiency of the mold filling simulation of die casting process. To speed up the convergence of the pressure field and speed field, the SOLA method was modified and a dynamic iteration direction method was put forward.

通过对SOLA算法中迭代方法的改进和采用"动态迭代方向"法，加速了流场计算的迭代收敛速度；通过引进"瞬态层"概念，大大简化了流场耦合温度场计算时的计算规模，提高了计算效率。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的&半收敛&性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

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。