迭代法

Elaborate a basic theory of calculating group of linear equation by iteration method, reforming Jacobi iteration method, raising constringency rate.

阐述用迭代法解线方程组的基本理论，对雅可比迭代法作了一些改进，提高了其收敛速度。

By using penalty function method, the iteration formulas of optimal design variables are derived, and the calculation procedure of the double iterative method is given in this paper.

利用罚函数外点法导出了优化设计变量的迭代计算公式，并给出了获得最优解的二重迭代法计算步骤。

By using accelerating Aitken method in iterative method of nonlinear equations, a new modified method is given. The method is applied to modified Newton method, thereby a new method is developed, which is faster and stable. Also, its algorithm is given. Numerical results show that the new method is very efficient.

通过对非线性方程组的迭代法引入Aitken加速技术，设计了一种非线性方程组的迭代解法的加速方法；将该方法与M步Newton法相结合，得到一种收敛速度快而且计算稳定的方法，并给出了具体算法；数值结果表明了新算法是有效的。

Iterative method with numerical integration, error under their control, using Newton iteration method.

详细说明：用迭代法计算数值积分，误差自己控制，用牛顿迭代法实现。

Based on prestressed steel beams, considering effect of the method of construction to slip and stress increment, accoding to conception that procedure of calculation reflects the procedure of construction and change of structural internal force, making good use of the method of section conversion and making iteration reflect the coupling of slip and stress increment, bringing forth a method of iteration and modified stiffness to calculate the deflection of prestressed composite steel-concrete beams in normal servicing prase.

以预应力钢梁为基础，充分考虑施工方法对结构滑移和应力增量的影响，依据设计计算中反映施工过程和结构受力变化过程，通过截面换算，以循环迭代法来考虑滑移和预应力钢束的耦合作用，提出了计算预应力钢—混凝土组合梁正常使用阶段挠度变形的迭代—修正刚度法。

In chapter one, firstly, we introduced several kinds of diagonally dominant matrices definition and their connection. Secondly, the relationship between those kinds of matrices and the convergence of some basic iteration methods (such as Jacobi, Seidel and SOR iteration methods) are also mentioned.

第一章，我们先简介了几类对角占优阵的定义及它们之间的关系，并介绍了一些基本迭代法(指Jacobi，Seidel及SOR迭代法等)的收敛性与这些矩阵类的关系。

A new simulation and optimization method using guass-seidel algorithm for cocurrent multi-effect evaporation was presented.

提出一种基于Guass-Seidel迭代法的多效并流蒸发过程的模拟以及优化方法，并以一简单三效并流蒸发过程为例，详细阐述了Guass-Seidel迭代法模拟的具体步骤。

Schur-Rayleigh-Ritz accelerated subspace iteration method: Schur-Rayleigh-Ritz accelerated subspace iteration method was applied to the gyroscopic eigenvalue problem.

2Schur-Rayleigh-Ritz加速的子空间迭代法将Schur-Rayleigh-Ritz加速的子空间迭代法应用于陀螺特征值问题。

In other words, a relaxation scheme is equivalent to a fixed-point iteration on a preconditioned system.

换句话来说，原线性方程组的松弛迭代法等价于预处理之后的方程组的定点迭代法。

An interesting observation is that the classical iterative methods can all be viewed as instances of an preconditioned system with different preconditioners.

值得注意的是，经典的求解线性方程组的迭代法也都能够看作是求解采用不同的因子预处理之后得到的线性方程组的迭代法。

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。