迭代的

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。

In this Chapter, we establish convergence theorem by using the majorizing method.

第二章，提出了一族具有三阶收敛迭代法，这族迭代法避免了求F的二阶导数。

Let C be a nonempty closed convex subset of a Hilbert space H, P:H→C be a nearest point projection, and T:C→H be a nonexpansive mapping satisfying the weakly inwardness condition, and :C→C be a fixed contractive mapping. Let the implicit iterative sequences {x},{y} and the explicit iterative sequences {x},{y}.

设C为实Hilbert空间H的非空闭凸子集，P：H→C为最近点投影映射，T：C→H为非扩张映象，且T满足弱内向条件，：C→C为压缩映象。t∈(0，l)，定义了2种隐式粘性迭代序列{x}，{y}和2种显式粘性迭代序列{x}，{y}，证明了T有不动点当且仅当序列{x}，{y}，{x}，{y}有界。

It can be found that the IPCA, as a non-iterative method, can obtain one principal component by only one calculating process. Therefore the IPCA is not only fast in calculation, but can avoid the cumulative error suffered by iterative methods.

使用模拟和实验HPLC-DAD数据对IPCA进行了验证，结果表明IPCA是一种非迭代方法，只需要完成一次计算过程即可得到一个主成分，因此IPCA不仅能够显著提高运算速度，而且可以避免迭代法中的误差积累问题。

The first step of IGA was to discretize time interval and control region to make the continuous dynamic optimization problem a discrete problem.

针对化工动态优化的数值求解问题，提出将迭代思想与遗传操作相结合，构建迭代遗传算法。

Expectedly the end product grows incrementally with new features, iteration by iteration.

果然，最终产品的增长逐步与新功能，通过迭代迭代。

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。

We also present iterated function systems 、local iterated function systems、Barnsley's collage theorem and Markov's theorem.

我们也介绍了迭代函数系统、局部迭代函数系统、Barnsley的拼贴定理和Markov定理。

By using the resolvent operator technique associated with relaxed-monotone operators, we construct a new iterative algorithm for solving the system of generalized mixed quasi-variational-like inclusions. We also prove the existence of solutions and the convergence of iterative sequences generated the iterative algorithm.

利用松弛－-单调算子的豫解算子技巧，给出了求解这类广义混合拟似变分包含组的迭代算法，并证明了由迭代算法生成的迭代序列强收敛于该变分包含组的精确解。

Chapter 8: We discuss the acceleration of multigrid by Krylov subspace approaches, and recognize the reason for slow convergence of algebraic multigrid methods is that error reduction is significantly less efficient for some very specific error components which may cause a few eigenvalues of the algebraic multigrid iteration matrix to be considerably closer to 1 than all the rest. However, the eigenvectors belonging to the few isolated eigenvalues can be expected to be typically captured after only a few conjugate gradient iterations, which accelerate algebraic multigrid algorithms. Theoretical analysis and numerical results of some practical problems show the iterant recombination accelerates algebraic multigrid convergence.

第八章：先介绍用Krylov子空间迭代法加速一般多重网格方法收敛的基本框架，然后紧紧抓住引起代数多重网格方法收敛减慢的根本原因往往是误差减小对几个特别的误差分量不明显，这导致代数多重网格方法的迭代矩阵的几个特征值接近于1，而共轭梯度方法则能比较典型地捕捉属于孤立特征值的特征向量，从而推导出有效的共轭梯度加速算法和程序实现，不仅从一些具体的实际应用例子的数值结果去验证迭代复合加速收敛的效果，而且还从理论上分析了预处理共轭梯度法加速代数多重网格法收敛的机理。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。