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Because of the problem of convergence, the key techniques to complete the one step simulation were explored thoroughly. The geometry mapping method based on finite element model and inverse deformation was developed to get the approximate initial blank for one step simulation. The effective selection of convergence factor in Newton-Raphson method was studied. The divergence criterion in iterative process for one step simulation was put forward. Also the countermeasure to ill equations coefficient matrix was studied.

由于存在收敛性的问题，本文重点研究了一步模拟方法计算机实现的关键技术：提出了基于有限元模型的几何映射方法和反向变形方法来确定初始毛坯的近似解，研究了带收敛因子的Newton-Raphson方法中如何高效地选取收敛因子，提出了一步模拟迭代求解过程中的发散准则，并研究了病态方程组系数矩阵的修正方法。

If the iterative step is greater than a certain number, the fictitious equilibrium force will change simply with factor of slope.The algebraic method is efficient to obtain a convergence value of safety factor.

研究结果表明：基于给出的算法，通过迭代求解安全系数，收敛速度快；在迭代初期，平衡力与安全系数间有较复杂的对应关系；当迭代次数大于某一值后，平衡力随安全系数的增加而单调地变化。

In chapter 1, we discuss several iterative methods and their convergence conditions. While, we also present the techniques in proving the convergence theorem.

第一章，主要对几种迭代法的收敛性进行了讨论，总结了它们的收敛条件及证明各种迭代法收敛性的技巧。

Fourthly, Broyden iterative method is studied to solve nonlinear equation with parameters and the existence and convergence theorem is also given.

第四章的主要结果：研究用Broyden迭代求解带参数非线性方程，在弱条件下给出Broyden迭代格式的存在性和收敛性定理。

The integral equation is convergent for any conductivity distribution and frequency if iterative solvers are used.

提出一种应用迭代法求解新积分方程的迭代初值优化选择方法，并通过具体算例对比说明该方法可使频率域电磁测深三维模拟的计算效率得到有效提高。

A integral equation formulation is derived based on modified Green's operator with norm less or equal to one. The integral equation is convergent for any conductivity distribution and frequency if iterative solvers are used.

利用范数小于或等于1的修正Green算子得到各向异性地层中的新积分方程，由于满足压缩映射条件，该积分方程在任意参数条件下总是迭代收敛的。

In this paper, we use the Pluricomplex Green function to investigate the iterative poperties of holomorphic self-maps, which are defined on the unit disk, the unit ball, the bounded strongly convex domain and the bidisc.

基于该思路，本文就利用多复Green函数，在分别研究了单位圆、超球、有界强凸域以及双圆柱上全纯自映射迭代的基础上，进一步研究了一特殊非凸域-Hartogs三角形上全纯自映射迭代的性质。

A Lipschitz strictly pseudocontractive map from a nonempty closed convex subset of a Hilbert space into itself was showed to have fixed points, Ishikawa and Mann iterative sequences with errors of a Lipschitz strictly pseudocontractive map was introduced and the iteration processes strongly converges to a fixed point was proved.

证明了在Hilbert空间中的非空闭凸集上Lipschitz严格伪压缩映象有不动点，介绍了Lips-chitz严格伪压缩映像下的的具误差的 Ishikawa和Mann迭代序列并证明了其强收敛性于不动点，其结果把非扩张映像推广到Lipschitz严格伪压缩映象上，改进了一些相关结果。

A complex thermal optimal mathematical model and a numerical iterative calculation method of multi-parameter function coordinate transformation are developed.

作者创造性地提出了迄今在理论上最为完整的溴化锂吸收式机组热力优化设计计算数学模型以及基于多元函数坐标轮换法的数值迭代计算方法。

The method based upon semi-infinite slopes is intended to approximate the prescribed transfer function. In order to minimize the error function, the least square method is adopted. The method of correction with term by term is used to avoid the divergent difficulties in iterative design.

本文提出以折线法来构造网络的逼近函数，并利用最小二乘法和逐项修正法相结合的办法来达到最优逼近，然后依据网络综合的理论，用RC网络的综合步骤来计算出实际元件值。

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。