求解过程

Use all PCA Gaussian elimination of linear equations, the solution process simulation and numerical calculation.

利用全主元高斯消去法对线性方程组的求解过程进行数值模拟与计算。

A clustering analysis method is used in the optimization of observed gravity data during the computation of local geoid.

针对局部大地水准面的求解过程，将聚类分析方法用于重力观测数据的优化设计。

In the third section of this paper, on the comprehensive study of some properties of proper k-vertex-coloring、 k-edge-coloring、 and total-coloring of a graph, the standard genetic algorithm for graph coloring is researched.

在本文的第三章节中，在系统分析了图的正常k－顶点着色、k－边着色和全着色问题的基础上，对基于遗传算法的图的着色问题的求解过程进行了深入的理论分析。

Boundary value problems in classical hydrodynamics are usually transformed from the physical plane to velocity plane by hodograph method.

在古典水动力学中，对於二维、稳态、不可压缩、无旋流场且不考虑其他外力影响之平面射流问题，常用速度矢端图法将其由物理平面转换至速度平面，再以复变函数法求得平面射流问题之自由流线参数方程式，但其求解过程甚为繁复。

With rules for basic topology identification and underutilized links elimination, the engineering experience can be imported into the algorithm to guide the searching for practically optimal solution.

通过基准拓扑确定、冗余链路删除等规则的设置，可以在求解过程中方便的引入工程设计经验，引导算法进行高效搜索，避免考察工程上"无效"的解空间。

This method, based on the physical characteristics of clould, such as incompressibility, low density and inviscid, uses the fluid equations to calculate the properties of cloud. Then by accelerating this method through GPU, it achieves a good effect, which is continuous, dynamic and real cloud .

首先分析了云的物理模型，考虑到GPU的特点建立了云的模型；然后根据云的不可压缩、低密度、无粘性的特点，通过流体方程计算了云的物理属性，并将其求解过程在GPU中实现，从而得到了动态的，真实感强的，实时的统一，得到了较真实的模拟效果。

Due to the problems existing in simulation on physical model of fire, such as heavy calculation, high complexity and difficulty in real-time simulation, a new real-time simulation method was raised based on fluid model and GPU acceleration. This method, based on the physical characteristics of fire, such as incompressibility, low density and inviscid, used the fluid equations to calculate the properties of fire. Then by accelerating this method through GPU, the real-time simulation of fire was realized and a realistic effect was achieved.

针对目前基于物理模型模拟火焰的计算量大、复杂度高，很难进行实时模拟的问题，提出了一种基于流体模型和GPU加速的火焰实时模拟方法，该方法根据火焰的不可压缩、低密度、无粘性等特点，通过流体方程计算火焰的物理属性，并将其求解过程在GPU中并行加速，从而大幅度提高了算法的运算速度，实现了火焰的实时模拟，并取得了较真实的模拟效果。

Additionally, in the process of calculating reliability index, the rational polynomial technique was introduced to solve the derivative problem of non-linear and inexplicit performance function.

在可靠指标的求解过程中，引入了有理多项式技术，解决了隐式求导的问题。

Because so many variables are involved in the model, the traditional optimization method is infeasible to solve it.

由于模型中涉及的参数过多，传统优化方法很难奏效，一种新的生物进化算法——遗传算法被引入到问题的求解过程中。

All computations involved are matrix operations in the linear algebra, and a closed-form solution can be obtained.

所提出的摄像机标定方法在求解过程中不需要非线性迭代，可以直接获得解析解。

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。