求解

The wavelet analytic method can find out global and local singularity and singular points of function by local maximum of wavelet transform of Lagrangian function which is made up of two constraint functions without regard for contents of optimization and constraint situation.

不管优化内容及约束情况如何，由对约束函数两两构成的拉格朗日函数的小波变换求局部极大值，将奇异点求解出来。本文对n维空间的小波变换寻优方法给予了理论上的研究与证明，并给出了具体的求解方法。

This problem is usually solved through Lagrangian relaxation, but this method is not effective in some situation.

因此，采用穷举法求解该问题，并通过实际的计算验证，使用穷举法可以很快求解出该问题的最优值。

The comparison study with the Laplace transform method of solving the transient temperature distribution and the finite difference method have discussed.

尤其对温度场的边界元求法、模腔的瞬态温度场分析进行了数学推导，对制品瞬态温度场的拉普拉斯变换法求解和有限差分法的求解进行了对比。

A left null factor of derivative matrix is introduced, and the sliding surface and the control's parameterization can be obtained by sloving strict LMI.

引入导数矩阵的左零因子，使得滑模曲面及控制器参数的求解可经过求解严格线性矩阵不等式获得，在一定程度上简化了LMI方法在奇异系统变结构控制器设计计算中的计算复杂性。

The experiment results show that the genetic algorithm is effective for resource levelling problem.

对标准问题库PSPLIB中大量问题的求解实验结果表明，遗传算法是求解该问题的一种有效算法。

Based on the experiences in Computational Fluid Dynamics, the linear equation solver takes more than 60% CPU time of the whole process, therefore acceleration of the linear equation solver is a key element in enhancing the whole performance of CFD.

研究了基于非结构化网格通用输运方程的数值求解方法，包括输运方程的离散格式，边界条件处理方法，压力速度耦合SIMPLE求解方法，详细讨论了影响界面流量计算的重要因素。

Some special matrices and numerical characteristics related to iteration solutions of linear systems, convergence and comparison theorems of matrix splittings, preconditioning techniques for iteration solutions of saddle point problems are deeply studied in this thesis.

本文对与大型线性代数方程组迭代求解有关的特殊矩阵和数值特征进行了深入的研究，特别系统地研究了矩阵分裂迭代法的收敛性和比较理论及鞍点问题迭代求解预处理技术。

The forth algorithm is the same as the third one with an addition of finite termination criteria. Although the latter two algorithms have only linear rate of convergence, they are especially suitable for large-scale and sparse problems, with features of simple formula, small storage, sparsity preservation and easy implementation.

前者借助NCP函数把互补问题转化为等价的非光滑方程组，再用带参数的光滑方程组近似这些非光滑方程组，最后用牛顿型方法求解所得到的光滑方程组，希望通过光滑参数趋于零得到原来互补问题的解；后者基于等价不动点格式，构造了一个光滑迭代算法和一个具有有限终止性质的算法，虽然这种迭代算法仅有线性收敛速度，但由于其格式简单、存储量小、保稀疏性、非常易于计算机实现等特点，故较适用于求解大规模稀疏问题。

In chapter 3 constructs firstlya new differential merit function by a perturbation structure of VIP and study theproperties of this merit function.Based on this merit function,a continuation-typeNewton method is proposed,which use the technique of inexact linear search forassuring its global convergence,and improves essentially the method of Taji,Fukushima and Ibaraki which can only solve the strong monotone VIP,and has locallyquadratic convergent rate under some condition.

第三章利用变分不等式问题的一种扰动结构构造了新的可微效用函数，并研究了效用函数的性质；在此基础上，给出了一类求解一般单调变分不等式问题的连续型Newton方法CN，方法采用了不精确的线性搜索技术以确保整体收敛性，从本质上改进了Taji、Fukushima和Ibaraki方法只能求解强单调变分不等式问题的局限性，同时又保持了局部二次收敛率。

A algorithm for solving large-scale sparse group of linear equations is presented.

给出了求解大规模稀疏线性方程组的一个实用算法；该算法能够保持矩阵的稀疏性和减少存贮量，并且能够求解一些大规模的问题。

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。