数值算法

This paper improves and perfects the numerical solution of the ray equation .

改进和完善了已有的光线方程的数值解法，使得该算法更具可操作性，并且给出了两种变折射率光线追迹的图形。

Unfortunately, due to lack of time, the numerical error and stability analysis which is the key to developing accurate and robust algorithms are only treated superficially in the MIT undergraduate curriculum.

不幸的是，由于时间不足够，数值误差和稳定性分析是开发准确可靠的算法的关键，而它们只是很浅显地在麻省理工学院的本科课程涉及到。

Finally, a numerical example is given to show the effectiveness of the algorithm.

最后给出一个数值例子验证了这个算法的有效性和稳定性。

These two algorithms have not only solved certain function numerical integration problem but also have the accuracy quickly.

这两种算法不仅解决了某些函数的数值积分问题，而且具有快捷性、精确性。

The numerical solution of wave function is obtained by solving schrǒdinger equation of partical spin with symposium.

利用辛算法求解粒子自旋问题的薛定谔方程，得到波函数的数值解。

In order to describe the random-like feature of chaotic signal, the statistical analysis method for discrete time chaos system is studied. A domain iterative algorithm for numerical estimation of the invariant probability distribution is presented, which is the foundation for the statistical analysis and processing of chaotic signal.

针对混沌系统的随机性特征，本文研究了离散时间混沌系统的统计分析方法，并给出了一种基于Frobenius-Perron算子的区间迭代算法用于混沌映射不变分布的数值求解，该方法在样本数较少时，仍可以获得不变分布的良好估计，为混沌信号进一步的统计分析和处理奠定了基础。

Numerical results show that the method is efficient.

数值实验表明该算法是十分有效的。

Finally,series of numerical experiments are made with the method mentionedabove.

最后，应用自适应叉树结构直角网格算法进行了一系列的数值实验。

First, a series of numerical analysis experiments are designed to investigate the effect of process variables on the damage factor, which constructs the learning samples for training the artificial neural network.

将基于数值模拟、人工神经网络和遗传算法的优化方法应用到镁合金的挤压工艺参数优化中，实现了镁合金挤压工艺设计过程中的参数优化问题。

In this paper,the method of interpolation for the numerical solution of tridiagonal system of linear equations is popularized,and another method of interpolation for quasi-tridiagonal system of linear equations is proposed.

文章将求解三对角线性方程组数值解的插值法进行推广，得到一种求解拟三对角方程组的插值算法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。