An eigenvalue interlacing theorem is given and proved . each eigenpair is computed by bisection and generalized rayleigh quotient iteration . for computing all eigenvalues and eigenvectors is o ( n2r2 ) , it is less than o ( n3 ) , which is the computational complexity of lapack , when r n 在计算全部特征值和特征向量的情况下，算法的计算复杂性为o ( n ~ 2r ~ 2 ) ，当r n时，优于坛一一一~一续攀遨粼望廷二生掣夔lapack的计算复杂性o ( n ’ ) 。
An equivalent integral programming model and a new semidefinite programming relaxation for the max - bisection problem are given . then , we solve the relaxation with a projected gradient algorithm . coupled with the randomized method , an approximate solution of the max - bisection problem is obtained 2 .给出图的最大二等分问题的整数规划模型的等价模型及其新的半定规划松弛模型,利用投影梯度算法求解该半定规划松弛模型,然后利用随机扰动算法求得原问题的次优解
By studying the solution to generalized effective medium satori resistivity model in laminated and dispersed shaly sand , it shows that there is a local minimum of the function about w derived from the model in the range from 0 to , and the w corresponding to the minimum varies with or w as well as other parameters , therefore , in order to ensure the iteration convergence , here , we adopt a hybrid algorithm combining newton and bisection , and the calculated result shows that using the hybrid algorithm to solve the equation about w is convergent . it is pointed out that shale distribution largely affects water saturatio n predicted by this model 通过研究混合泥质砂岩有效介质通用satori电阻率模型的求解方法，表明模型导出的关于_ w函数在0 -区间内存在一个局部极小值，且该极小值点对应的_ w随或_ w及其他参数的变化而变化，因此，为了保证迭代收敛，采用牛顿和二分结合的混合迭代算法，试算结果表明利用牛顿和二分混合迭代算法求解关于_ w的方程是收敛。
In the simulation of functions , this method performs better than chaotic optimization algorithm . with the combination of bisection - interpolation approach and gauss newton levenberg - marquardt method , we optimize neural network and fuzzy inference system . taking advantage of bisection - interpolation approach , simulated annealing algorithm and genetic algorithm find the better solution than chaotic combination method 作者通过大量的函数仿真以及将其与牛顿高斯levenberg一manquardt方法、模拟退火、遗传算法等常用算法相结合，形成的混合优化算法，对神经网络、模糊神经网络和函数进行了优化，其优化效果明显优于混饨以及混饨混合优化算法。
To illustrate the feasibility and verify the isolation and re - centring effect of the above system , a series of theory analysis and calculating program is presented in this paper . the following work is done : first , because the constitution relation of shape memory alloys is expressed by differential equation , solving the equation becomes unusual complex . the method of bisection is introduced to carry though value calculation , in this way , the relation of stress and strain is revealed 为了验证上述隔震体系的可行性和合理性，检验其隔振与复位效果，本文进行了一系列理论分析与程序模拟，主要内容有：首先，针对形状记忆合金本构关系中复杂的微分方程组，提出了一种采用对分法的数值求解方法，以得到形状记忆合金材料相变伪弹性过程中的应力?应变关系，编制计算机程序并进行了数值模拟。
There are many faults in the chaotic optimization algorithm . to solve these problems , a new method named " bisection - interpolation approach " is put forward . it has numerous advantages such as ergodicity , uniform distribution , not sensitive to the change of initial value , not sensitive to the defining range of variable , not requiring the continuation and not requiring differential of the optimized object 该算法和混饨一样具有遍历性的特点，且变量均匀分布于定义域，对函数的定义域变化和初值的选定都不敏感，同样也不需要函数连续、可微，对优化对象几乎没有特别要求，从而避兔混池优化算法的缺点。
Executing the lifting method to the equivalent programming , we present a strengthened semidefmite relaxation . as predicted by theory and confirmed by numerical experiments the tight semidefinite relaxation gives a better lower bound of circuit bisection than the one that the previous semidefinite relaxation gives 本文先通过增加非线性约束得到原始问题的等价模型，进而对等价模型利用提升技术，提出了一个强化的半定松弛模型；最后，将结果推广到更具一般性的图的分割问题。
In the paper , we firstly summarize the theory , algorithm , application and recent research of semidefinite programming , then , introduce our some work in algorithm and application . for detail , we conclude them as follows : 1 . a nonlinear programming algorithm was proposed for the max - bisection problem , and the convergent result was given 本文首先介绍了半定规划的基本知识,包括半定规划的理论、算法、应用和研究现状,然后在半定规划的算法和应用方面做了一些工作,具体如下： 1 .对图的最大二等分问题提出一种非线性规划算法,并给出该算法的收敛性证明
To inaugurate a series of static , semistatic and peripatetic intellectual dialogues , places the residence of both speakers if both speakers were resident in the same place , the ship hotel and tavern , 6 lower abbey street w . and e . connery , proprietors , the national library of ireland , 10 kildare street , the national maternity hospital , 29 , 30 and 31 holles street , a public garden , the vicinity of a place of worship , a conjunction of two or more public thoroughfares , the point of bisection of a right line drawn between their residences if both speakers were resident in different places 开始一系列静止的半静止的逍遥的理性的对话，在对谈者双方家中倘若对谈者双方住在同一处位于下阿贝街六号的“船记”饭店兼酒馆经营者为w和e .康纳里，基尔代尔街十一号的爱尔兰国立图书馆霍利斯街二十九三十与三十一号的国立妇产医院，一座公共花园，礼拜堂附近，两条或更多的街道交叉点，连接双方住宅的直线的中点倘若交谈者各住一处。
Combining multilevel scheme , spectral bisection method , kl / fm refinement , as well as multi - partitioning refinement strategy , the computing method is characterized by high efficiency , flexibility , and simplicity because it both maintains load balancing and minimizes the complexity of communication among processors 算法结合了多层次思想和谱分区方法、 kl fm精化算法和多分区调整策略等技术，以保持负载平衡和减小处理器之间的通信复杂度为目标，具有高效、灵活、简便等特点。
