迭代法

This paper is made up of three chapter, which discuss mainly about the astringency of the iterative methods and the application in fact.

本文共分三章，主要讨论的是迭代法的收敛性及其在实际中的应用问题。

The iterative method is the most important and convenient one for solving equations in the form of F =0 (1) in Banach space.

迭代法是解Banach空间中形如 F=0 (1)的方程的最重要最便利的方法。

In order to get the exact value of the Hopf bifurcation point, we discuss the discrete version of the integro-differential equation, and use the approximation parameter as the initial value of the Newton iteration method.

为了得到Hopf参数的精确值，进一步讨论了延迟积分－微分方程的离散形式，利用Newton迭代法，得到了参数的逼近值。

It is related to the variational inequality problem, bilinear programming, nonlinear equation. So there is actual meaning and theories value to study how to solve it.In recent years, many algorithms for solving the generalized linear complementarity problem are put forward. But they basically belong to the traditional iterative methods, and may not be efficient since the computing time required for a solution is greatly dependent on the dimension, structure of the problem and the complexity of the algorithm used. Different from the traditional algorithms, the neural network has many advantages on calculations and real-time applications for its inherent massive parallelism and electric circuit implementation.

近年来，人们对广义线性互补问题提出了许多算法，但这些方法基本上属于传统的迭代法，由于它们的计算时间极大地依赖于问题的规模、维数以及所使用的算法，因此很难满足实时并行的要求，与传统数值方法不同，由于内在的并行分布处理信息的特点及电路实现的潜能，神经网络有着许多计算上的优势和实时性的应用，自Hopfield提出著名的人工神经网络模型-Hopfield神经网络，并将其成功应用于优化问题后，用神经网络求解优化问题得到了相当深入的研究，并取得了许多重要的成果。

By central difference in time and space and boundary conditions, equilibrium equations of warp are transformed into the definite equations and solved by Newton\'s iteration.

通过在时间和空间上对拖网曳纲平衡方程组进行中心差分以及首尾边界条件的处理，将该方程组转换为定解代数方程组，并采用牛顿迭代法求解。

Integral iteration method is a kind of stable downward continuation method for potential fields.

积分-迭代法是一种解决位场大深度向下延拓的实用方法。

Practical calculation shows that the proposed method can improve the convergence under large power angle conditions and also reduce the computing time by more than 80 percent.

实例计算表明，场路耦合端点量迭代法能改善大功角稳态工况下算法的收敛性，并使计算时间缩短了80%以上。

In view of the tedious and mistakable manual calculation in measuring Gauss projection,coordinate zone transformation and meridian convergence,an itera-tive approximation method is adopted and programmed by BASIC to imple-ment the direct and converse calculation of Gauss projection and computer cal-culation of meridian convergence angle.

针对测量工作中人工进行高斯投影、坐标换带和平面子午线收敛角计算非常麻烦又容易出错的问题，采用迭代法趋近求值，用BASIC语言编制了相应的计算机程序，实现了上述计算。

In chapter 3,we establish convergence theorem under Ostrowski-Kanorovich condition for Newton-like method by using majorizing method.

第三章：通过运用优函数的方法，建立了Newton类迭代法在Ostrowski-Kantorovich条件的收敛性定理，并给出了相应的误差估计。

To improve this point, a method based on the cosine basis and the successive over-relaxation is developed in this paper.

基于这一点，该文提出了一种采用余弦基和逐次超松弛迭代法的闪烁去除方法。

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。