迭代的

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。

This thesis consists of two parts. The first one was that boundary value problem was discrete with five point difference method. Three kinds of memory formats were studied, which were full matrix, half band width and row compress sparse. Full matrix memory format and half band width memory format first was contrasted. The results show that half band width has efficiency in space. Then the algebraic system of finite element method was solved by Gauss-Seidel iteration method to popular row compress sparse memory format.

本论文由两部分组成，第1部分针对边值问题，用5点差分格式进行离散，并对离散矩阵这类大型稀疏矩阵，研究了系数矩阵的3种存储格式的优劣，即：满矩阵存储格式、半带宽存储格式和按行压缩稀疏存储格式，首先我们将满矩阵存储方式和半带宽存储格式进行了对比，迭代法的数值实验表明：利用半带宽存储的矩阵在空间运算方面具有高效性；然后针对目前数值实验中流行的按行压缩稀疏存储格式，实现了有限元离散代数系统的迭代法的求解。

First, a special normal transversal at the initial point is constructed and a second-order Taylor's algorithm is used to trace the projections along the aforementioned normal transversal. A curvature based method for controlling iteration step is further proposed by projecting the given point onto the curvature circle of the normal transversal at the initial point. Finally gradient based method for correcting iteration errors is put forward.

首先构造初始点处的一条特殊的法截线，并给出沿着该法截线追踪投影点的二阶泰勒迭代方法；然后将给定点向初始点处的法截线的曲率圆作投影，提出基于曲率的步长控制策略，在此基础上给出了基于梯度的迭代误差矫正方法。

If the Landweber method and pre-iteration method were convergent, the residue sequence would be monotone decreasing. By analyzing the convergence, the fact is demonstrated that for the severe ill-conditioned matrix of sensitivity coefficient, because of the limitation of the precision of the computer, the residue sequence is not monotone decreasing; thereby the reconstruction images diverge from the true distribution of the conductivity. So the generalized inverse method with threshold is established and the selection way of the regularization parameter is presented, by which the better images are reconstructed.

Landweber法和预迭代法收敛，则其残差序列单调递减，通过对它们的收敛性进行分析，证实对于病态性严重的灵敏度系数矩阵，由于受计算精度的限制，迭代过程中的残差序列不再单调递减，从而导致重建图象偏离实际电导率分布，因此作者建立了带阈值的广义逆算法，提出了规则化参数选择方法，获得了较好的图象重建质量。

In a proper condition, U(superscript *) is a generalized solution of the differential equation system.

提出了象凸微分方程组的概念，并用这一概念对一类微分方程组的边值问题提出了一种新的变分迭代解法，此迭代解的极限U存在；在适当的条件下，U为此微分方程组的广义解，应该指出：1。

It Newton iteration is used in the analysis of math value,and the simplicity formula is given to resolve(including original initial value formula and advanced approximation formula),which can be characterized by fast speed and easy remembering.

采用数值分析中的牛顿迭代法求反渐开线函数的根，并给出了符合精度要求的解算反渐开线函数的简单公式(包括原始初值公式和近似值精化公式)，具有迭代收敛速度快、简单易记的优点，它们适用于[0，π/2]的全区段，免除了分段计算的烦恼，并运用VB编写计算机程序，从而实现反渐开线函数快速求根的目的。

Introduce the ideological root causes and background knowledge in detailed, give the iterative formula and the iteration step.

针对微粒群算法在求解函数优化问题时出现的一系列问题，本文提出了雁群算法，详细介绍了雁群算法的提出的思想根源和背景知识，给出了算法的迭代公式和迭代步骤，并结合具体实例与微粒群算法相比较，对于某些优化问题，其优化性能比微粒群算法有较大的提高，在一定程度上弥补了微粒群算法的不足。

In this paper, an iterative approach to potential field continuation from curved surface to plane is proposed. The continuation of potential field data from a curved surface to a plane can be viewed as an inverse problem of upward continuation of plane potential field data, getting a linear integral equation. Through viewing the potential field data on the curved surface as the data on the average elevation plane of the curved surface, then using the wavenumber domain generalized inverse algorithm to downward continue the data from the average elevation plane to a given plane, and a topography correction based on the change of curved surface relative to its average elevation is implemented to the downward continued data on the given plane, finally the downward continued data plane is upward continued to the curved surface.

本文提出一种位场数据曲化平的迭代方法，即通过把位场数据曲化平视为平面位场数据向上延拓的反问题，得到曲化平的线性积分方程，再把曲面上位场数据视为曲面平均高程面上的位场数据，利用向下延拓的波数域广义逆算法把平均高程面上的位场数据向下延拓到设定平面上，再根据曲面和其平均高程面的相对起伏对设定平面上的向下延拓数据进行起伏校正，最后再把所得平面上的位场数据向上延拓得到曲面上的位场数据，并进行迭代。

We construct a kind of special matrix function, which is used to characterize the minimization property of this iterative method, and prove that the approximate solution, generated by this iterative method, minimizes this kind of matrix function over a special affine subspace, which means that the Frobenius norm of the residual sequence is strictly monotone decreasing.

通过构造一类特殊的矩阵函数来刻画该迭代方法的极小化性质，并证明了由该迭代方法计算出来的逼近解，可使得这类矩阵函数在一个仿射子空间上达到极小，而且所得到的残差序列的Frobenius范数是严格单调递减的。

These eigenvalue algorithms are examined under the mode error, i.e, the ratio of out-of-balance nodal point forces that is the difference of maximum elastic nodal point forces and maximum inertia nodal point forces, and the maximum elast...

与ANSYS的子空间迭代和Lanczos法相比，本文的子空间迭代比ANSYS的效率高很多，Lanczos法和ANSYS的效率差不多。大量较大规模的例题显示，本文对特征值算法的改进是十分有效的，算法的健壮性，通用性都达到了高水平。

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。