数值算法

For overlapping domain decomposition method, we prove the geometric convergence for continuous algorithm in the sense of energy norm by means of projection theory, analyze the convergence rate of the algorithm in detail. And we also discuss the discretization of the algorithm and its finite element implementation. Some numerical experiments are also given.

对重 叠型区域分解算法，利用投影理论，证明了连续型算法在能量模意义下的几何收敛性，详细地分析了算法的收敛速度，也讨论了算法的离散化及有限元处理，并给出了相应的数值实验。

For this purpose, the compactly supported radial basis function and the moving least squares approximation based ones are integrated into the aforementioned two global optimizers. As a result, two novel hybrid algorithms are introduced.

其次，为解决电磁场逆问题分析、计算中由于随机类优化算法需进行数以千计次电磁场的数值分析，以致计算时间和计算量难以满足工程分析实际要求的难题，本文将表面响应模型法引入电磁场逆问题的求解，研究了基于紧支径向基函数和基于移动最小二乘法的两种表面响应模型，并将其分别与改进的遗传算法和粒子群算法相结合，提出两种不同的混合快速全局优化算法。

The results of numberical simutation show that the new algorithm is more effective than the other algorithms.

该算法弥补了仅用罚函数作为遗传算法的适应函数之不足，数值模拟结果表明该算法比其他算法更加有效。

This article introduced the C # language used to generate a straight line of three commonly used method: numerical differentiation, in line and stipple Bresenham algorithm, and then introduced the mid-point algorithm Circle, the polygon algorithm.

本文主要介绍了用C＃语言生成直线的三个常用算法：数值微分法、中点画线法和Bresenham算法，然后介绍中点画圆算法、多边形的生成算法。

The superlinear convergence property of the algorithm is proved in this paper, and compared with the Tensor algorithm. It is proved that this method is more efficient for solving unconstrained optimization whose object function is of rank one defect.

文中证明了该算法是一个具有超线性收敛的算法，并且把修正的BFGS算法同Tensor方法进行了数值比较，证明了该算法对求解秩亏一的无约束优化问题更有效。

In this paper, the maximum likelihood algorithm with process and measurement noise for nonlinear continuous-discrete system given by Jategaonkar and Plaetschke is improved in two aspects: 1 to avoid the disadvantages of sensitivities computation by common finite-difference method, in which the perturbation sizes should be selected optionally, an improved finite-difference method with best perturbations, is presented. 2 to improve the numerical stability of Jategaonkar's algorithm, maximum likelihood algorithm with fast triangular square-root decomposition filter is given.

摘要对Jategaonkar等人给出的同时计及过程及观测噪声的非线性连续-离散系统的极大似然算法从两个方面进行了改进：1给出了计算灵敏度的最佳摄动有限差分算法，避免了普通有限差分法计算灵敏度矩阵时需人为选择参数摄动量大小而带来的缺点；2给出了具有快速三角化平方根滤波的极大似然算法，提高了原算法的数值稳定性。

With the guide of non-linear program theory, by using interpolative steps and inexact line search, an improved conjugate gradient method was found, by which the training rate of BP networks increases by tens or hundreds of times. Moreover, the improved method is effective to solve non-linear equations for which Newton's method does not converge owing to the problems of the quadratic derivative and inverse matrix.

通过大量的数值模拟试验发现，在非线性规划理论的指导下采用间插步骤和不精确的一维搜索技术改进的共轭梯度法，是基于梯度和共轭方向的连续搜索算法中最有效的算法，这种算法使BP网络的训练速度提高几十到几百倍，使BP网络的实际应用效果大为改善；而且这种算法对于用牛顿法由于求二阶导数和求逆矩阵等问题难于收敛的非线性方程组的求解也是很有效的。

In this paper, the generator model of constant transient voltage and the invariableness impedance model was used, and the saliency of generator is included; through the analysis of the characteristic of the network equation calculation in the transient stability analysis, a new node ordering algorithm is proposed. Better initial value can accelerate the convergence rate of the networking equations, reduce the number of iterations, thus to cut down the amount of calculating time.

本文首先建立了适合于暂态稳定分析的简单模型，其中发电机采用E_q恒定模型，考虑了发电机的暂态凸极效应，负荷采用恒定阻抗模型；研究了电力系统的暂态稳定分析方法，指出目前数值积分暂态稳定计算方法中存在的不足，主要是网络方程的求解速度过慢；分析了暂态稳定计算中网络方程的特点，将稀疏技术应用于网络方程的求解，提出了一种新的节点编号方法——最小度最小有源节点道路集算法，减少了网络方程的计算量；在进行交替迭代求解时，将预测算法应用于每一积分步网络方程功角和电压的初值估计当中，应用自回归算法和广义延拓算法，期望给出一个更有效的电压和功角初值方案，来加快方程的收敛过程，减少方程迭代的次数，以提高计算速度。

The multiresolution time-domain algorithm based on the scaling function of the Daubechies wavelet is introduced, and the perfectly matched layer absorbing boundary condition for the algorithm is deduced. In order to overcome the difficulties due to the nonlocalized property of the MRTD basis functions, the pure scattered-field formulation is adopted. The method presented is applied to the scattering analysis of multiple conducting objects, and the numerical results are compared with those by the traditional finite-difference time-domain method. It is shown that the computational resource is reduced drastically without sacrificing much accuracy.

对基于Daubechies小波尺度函数的时域多分辨分析算法进行了详细论述，推导了MRTD算法的完全匹配层吸收边界条件，为克服传统MRTD方法中基函数存在着非局部性的缺点，在源的加入上采用了纯散射场方法；并应用该算法对多目标的电磁散射特性进行了分析，数值结果表明，MRTD算法与传统的时域有限差分法结果相吻合，大大节约了计算资源。

GA often uses C or Visual C++ to compile codes, so the program is not only long and cockamamie but also the efficiency is low and the velocity is slow. This paper uses software Matlab powerful calculating ability and many functions to compile programs, then encapsulate and link those programs to run without Matlab environment. At last use Visual C++ friendly alternate function to compile in-out interface.

针对遗传算法常用C或Visual C++编写源代码，程序庸长繁琐，效率不高，运行缓慢的特点，本文采用Matlab强大的数值计算能力和众多的库函数编写算法；然后封装和链接程序，使Matlab编写的算法能够完全脱离Matlab的编程环境；利用Visual C++良好的人机交互功能，用Visual C++编写算法的输入输出接口界面。

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。