迭

For solving the linear system with the iterative method, it is very important to estimate the spectral radius of the iterative matrices.

在用迭代法解线性方程组时，迭代矩阵的谱半径估计在迭代法的收敛性分析中起着重要的作用。

Puthermore,we make a comparison between its optimum spectral radius and that of SOR method and draw a conclusion that these two methods have their own advantages respectively under different conditions.

除了对迭代方法的研究和改进，对方程组本身做某些处理，如对它进行预条件也是有效改善迭代收敛性，加快迭代收敛速度的方法之一。

when computing the next tracing point, the traditional tracing method generally used the iterative method. but the iterative method had to face the following problems.

摘 要：传统的跟踪方法在求下一个跟踪点时一般是采用迭代法，而迭代法会出现初始值的选取和迭代收敛的问题。

In orderto improve the complex subspace iteration method for solving undamped gyroscopiceigenvalue problems, we apply the special properties of undamped gyroscopiceigenvalues to it, so we propose double inverse iteration method and double subspaceiteration method.

为了利用无阻尼陀螺特征值的特殊性质，我们进一步讨论了复子空间迭代法在无阻尼陀螺特征值问题中的应用，并给出了双逆迭代算法和双子空间迭代算法。

In this paper,first,a formula of the esˉtimation of functional iteration is discussed and a resultwhich is better than old one is obtained.Then a question of iterationlimit of functional serieses and uniform convergence is discussed.

首先讨论了函数迭代估计的一个关系式，得到了函数迭代估计的一个更好的结果；然后研究了函数序列在一致收敛下的一个迭代极限问题。

There are large niche overlaps between the shrub and semi-shrub species and among the herbaceous plants of which the overlap between H. scoparium and A. ordosica and between Chloris virgata and Bassia dasyphylla were 0.7192 and 0.8622, respectively, and this indicates that they have greater ecological similarity thus possessing strong competitive capacities in community succession; there are smaller niche overlaps between A. ordosica and various herbaceous plants and thus they can stably co-existed.

灌木、半灌木种之间、草本植物与草本植物之间的生态位重迭值较大，其中花棒与油蒿、虎尾草与雾冰藜之间的生态位重迭值分别为0.7192和0.8622，这表明二者之间有较大的生态相似性，从而在演替过程中具有较强的竞争作用；而半灌木油蒿与各草本植物之间的生态位重迭值很小，它们能够实现稳定共存。

When the matrix equation is consistent, its centrosymmetric solution can be obtained within finite iterative steps in the absence of round off errors for any initial centrosymmetric matrix X1, and its least-norm centrosymmetric solution can be derived by choosing a suitable initial iterative matrix.

当矩阵方程AXB+CXD=F有中心对称解时，在有限的误差范围内，对任意初始中心对称矩阵X1，运用迭代算法，经过有限步可得到矩阵方程的中心对称解；选取合适的初始迭代矩阵，还可以迭代出极小范数中心对称解。

If one is provided, it must be an iterable, i.e., a sequence, an iterator, or an object that supports iteration such as a file or a dictionary.

如果提供一个参数，则该参数必须是可迭代的，即，一个序列，或迭代器，或支持迭代的一个对象，例如：一个文件或一个字典。

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。

AIM: To investigate the inhibition capacities of carnosol, rosmanol, and epirosmanol, which are phenolic diterpenes from Rosmarinus officinalis, to oxidized low-density lipoprotein formation in human blood and detect their scavenging activities to lipid free radical and superoxide anion in vitro.

目的：研究迷迭香中二萜酚化合物鼠尾草酚、迷迭香酚和表迷迭香酚对人低密度脂蛋白氧化的抑制作用及其对自由基和超氧阴离子的清除作用。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。