迭代法

In Chapter 1, we summarize several iterative methods and their convergence condition, the techniques in proving the iterative methodss convergence theorem.

现在，迭代法的研究日益成为解决各种非线性问题的核心，迭代法优劣的选择直接影响到各种非线性问题的结果的良好，所以迭代法的研究有着十分重要的科学价值和实际意义。

It solves the grid equations with domain decomposing multigrid parallel method and precondithoners as elimination method.From the discussion of the iterative property of Gauss elimination method,it can improve the parallel efficiency by overcoming the obstacle in the information passing.

对网格方程组作多重网格区域分裂并行计算，以消去法为预条件，讨论了Gauss消去法的迭代性质，指出该迭代法有效改善通常迭代在子域信息传递过程中的障碍性问题，提高多重网格区域分裂并行计算效率。

On the other hand, we introduce the convergence theories for generalized alternating method, parallel synchronous iterative methods and parallel alternating synchronous iterative methods when the coefficient matrix are Hermitian positive definite matrices.

接着，讨论了当系数矩阵是Hermitian正定矩阵时广义交替迭代法，并行同步迭代法，并行交替同步迭代法的收敛理论。

By the principle of penalt function, the irrotational fluid field is constrained, and author has proposed the Difference Method for distinguishing fluid vortex modes among the natural modes of coupled systems. Author has calculated the real frequencies with the extra deductive method, and discussed the influence of the numerical solution due to the irrotational constraint.

对于流体有限扰动时的非线性耦合系统的有限元分析作了一些探讨，给出了非线性系统的基本方程、变分原理及有限元方程，并具体地导出了三维几何非线性流体单元的切线刚度公式，采用增量形式的Newmark预报——校正逐步积分法计算系统的动力响应，由Newton-Raphson迭代法及其修正方法求解系统的非线性方程组，还列出了不平衡力余量检查和位移迭代增量检查等迭代收敛判断准则。

In the second one, Jacobi method, Gauss-Seidel method and Successive Over-Relaxation method were compared under the three kinds of memory formats.

在论文的第二部分，我们比较了在三种存储格式下的迭代法，迭代法和迭代法的优劣。

This paper investigates alternating iterative method and generalized alternating method for the solution of a large linear system, extend the convergence theorem and comparison theorem for generalized or alternating iterative method when the coefficient are Hermitian positive definite systems.

本文主要研究了大型线性方程组的交替迭代法及迭代法的各种变形，给出了当系数矩阵为Hermitian正定矩阵时各类迭代法的收敛原理及其相应的比较理论。

Use c language to make a Jacobi iterative arithmetic which could solve the linear equation group, but it s may be more ...

求解线性方程组的迭代，是一种简单的迭代法，可不如 Gauss-Seidel迭代法收敛速度快。

Aitken Iterative procedure, similar to the simple iterative method, but due to simple iterative method.

详细说明： Aitken迭代程序，类似于简单迭代法，但由于简单迭代法。

Chapter 8: We discuss the acceleration of multigrid by Krylov subspace approaches, and recognize the reason for slow convergence of algebraic multigrid methods is that error reduction is significantly less efficient for some very specific error components which may cause a few eigenvalues of the algebraic multigrid iteration matrix to be considerably closer to 1 than all the rest. However, the eigenvectors belonging to the few isolated eigenvalues can be expected to be typically captured after only a few conjugate gradient iterations, which accelerate algebraic multigrid algorithms. Theoretical analysis and numerical results of some practical problems show the iterant recombination accelerates algebraic multigrid convergence.

第八章：先介绍用Krylov子空间迭代法加速一般多重网格方法收敛的基本框架，然后紧紧抓住引起代数多重网格方法收敛减慢的根本原因往往是误差减小对几个特别的误差分量不明显，这导致代数多重网格方法的迭代矩阵的几个特征值接近于1，而共轭梯度方法则能比较典型地捕捉属于孤立特征值的特征向量，从而推导出有效的共轭梯度加速算法和程序实现，不仅从一些具体的实际应用例子的数值结果去验证迭代复合加速收敛的效果，而且还从理论上分析了预处理共轭梯度法加速代数多重网格法收敛的机理。

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 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。