迭

MGM is introduced to solve field distributions in 3-D electron optical systems. The difference equation, the discrete form of Laplace's equation, is deduced in 3-D Cartesian coordinates. In view of the smooth effect, MGM combines Gauss-Seidel iteration with a technique known as coarse grid correction. Formulae for restriction and prolongation are deduced and expressed in terms of tensors.

将多重网格法引入电子光学系统中三维静电场的计算，对三维笛卡尔坐标系中的差分方程，采用高斯-赛德尔迭代法求解差分方程组，并结合迭代过程讨论了粗网格的误差校正技术；在不同网格层之间进行场值的限制和延拓，推导了三维静电场中的限制、延拓公式并以张量的形式表示。

However, we can use the initial estimate to make a rough sketch, or release plan, of what work will happen in each iteration and how many iterations will be needed.

但是，我们能够根据初步估计，画出草图，或者发布计划。而这些草图或发布的计划展示了每个迭代周期内所需的工作量以及所需迭代周期的数量等等。

Finally by constructing an auxiliary problem, using addition theorem and applying an iterative process based on results obtained for the linear problem, the existence and uniqueness of the weak generalized solution of the nonlinear problem is proved.

解决了线性问题后，本文构造了辅助问题，利用迭加原理，并基于线性问题的主要结论运用迭代过程，最终证明非线性问题存在唯一广义弱解。

The relationships between the eigenvalues of Jacobi iteration matrix and the block AOR iteration matrix make a very important role in our analysis. Then we prove some sufficient conditions for the semiconvergence of the block AOR method.

利用块AOR迭代矩阵和相应的块Jacobi迭代矩阵的特征值之间所存在的关系，我们证明了求解奇异p-循环线性方程组的块AOR迭代法半收敛的一些充分件。

By reformulating each pass in the original algorithm into two sub-passes, we make the new algorithm suitable to be implemented on GPU. Additionally, we reduce the number of the conditional branch instructions involved in the improved algorithm, taking advantage that there are a large number of similar conditional branch instructions between two sub-passes.

我们对原算法进行细化，将每一次迭代分为两次子迭代，以满足GPU中并行处理的要求，并进一步在子迭代中减少条件判断的次数。

Many questions in natural science and engineering canbe transformed into nonlinear equations to be salved,Newton iterative method is an important technique to one-and multi-dimensional variables and iterative process exhibits sensitive dependence on initial guess point.

自然科学与工程中的许多问题都可以转化为非线性方程组的求解问题，牛顿迭代法是重要的一维及多维的迭代技术，其迭代本身对初始点非常敏感。

I obtain more accurate results such as, the convergence for JOR. In 3.4, I analyze the convergence of SOR.In 3.5, I study the convergence of MSOR.

如3.3节JOR迭代法的收敛性分析 3.4节研究了SOR迭代法的收敛性分析3.5节研究了MSOR迭代法的收敛性分析

The downward continuations are made by the iteration method and the FFT for a model and practical data, respectively. The effect of the iteration method is much better than the FFT.

本文用迭代法对模型数据和实际数据进行向下延拓，对比了迭代法与常规的FFT法在位场向下延拓中的效果，迭代法显著优于FFT法。

The algorithm is implemented by a three-stage iterative process. At the first stage, an iterative block matching algorithm is applied to generate more accurate initial disparity vectors, and at the second stage, an iterative polygon matching algorithm is employed to optimize the initial disparity vectors obtained at the first stage to minimize the error of certain triangulations. Finally at the third stage, the unreliable nodes are deleted.

该方法是一个三步迭代过程：首先利用迭代块匹配算法得到较精确的匹配结果；然后利用迭代多边形匹配算法对得到的匹配结果进行优化，使得一些三角形的预测误差最小；最后删除掉视差不可靠的节点。

However, the position results by using their iterative algorithm were non-convergent in the experiment. The formulas given by scholar Haworth, et al. are deduced carefully in this paper and some faults of their itera...

该文通过详细的推导，指出了Haworth等人迭代算法的失误，修改了Haworth等人的迭代算法，并通过实验验证了修改后的迭代算法的正确性。

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。