两相流重粒子运动的非线性系统方程组的计算

本文阐述两相流重粒子运动的非线性常微分方程组实际上代表一个系统的方程组,讨论了常用的解法如Runge—Kutta法等和它的结果。本文采取变步长用有限分析法把非线性项线性化,构造一个迭代序列,逐步迭代修正非线性项,求解一般形式的非线性系统方程;并验证迭代逼近解的收缩运算条件;给出计算重粒子运动轨迹和速度的算例,结果分析和说明应用的实例。     

用于双基地雷达目标定位的全局收敛高斯-牛顿法

考虑了双基地雷达目标定位问题中的非线性最小二乘方程组的迭代解法。用高斯 牛顿迭代法解非线性最小二乘方程组计算量小、收敛快,但所得解的正确性及精度依赖于选取的迭代初值与真值的靠近程度,及方程组的非线性强度。给出了两种变步长全局收敛策略,与高斯-牛顿法相结合可得到对初值不敏感的迭代算法。仿真结果表明,用全局收敛的高斯 牛顿法解最小二乘方程组能得到更准确的解,且迭代次数较少。     

RESIDUAL A POSTERIORI ERROR ESTIMATE OF A NEW TWO-LEVEL METHOD FOR STEADY NAVIER-STOKES EQUATIONS

Residual-based a posteriori error estimate for conforming finite element solutions of incom-pressible Navier-Stokes equations,which is computed with a new two-level method that is differentfrom Volker John,is derived.A posteriori error estimate contains additional terms in comparison tothe estimate for the solution obtained by the standard finite element method.The importance of theadditional terms in the error estimates is investigated by studying their asymptotic behavior.For opti-mal scaled meshes,these bounds are not of higher order than the convergence of discrete solution.Thetwo-level method aims to solve the nonlinear problem on a coarse grid with less computational work,then to solve the linear problem on a fine grid,which is superior to the usual finite element methodsolving a similar nonlinear problem on the fine grid.     

违约回收率密度函数模拟的非参数估计方法研究

本文研究违约回收率密度函数的模拟估计问题. 本文的工作由两个方面组成. 首先,我们解决了在应用非参数方法估计违约回收率密度函数时如何选取窗宽,以及在使用对称核时如何处理在有界区间上产 生的边界问题. 针对如何选取合理窗宽提高估计效果的问题,我们通过将最优窗宽选取通过渐近积分误差最小作为 标准,然后将满足渐近积分误差最小的问题转换为一个非线性方程,进而应用插入法与迭代算法,求出最优窗 宽的收敛解. 第二,针对应用普通对称核拟合分布于[0,1] 区间内的回收率会产生的估计量偏差在边界有增大趋势问题,我们通过引入边界核来改善这一现象：首先对两种核的统计性质进行理论推导,随后使用蒙特卡罗模拟（Monte Carlo Simulation）方法对其拟合绩效进行数值分析. 本文的数值结果表明我们引入边界核方法,这较之普通对称核可以有效改善边界问题,同时边界核方法在各个指标上效果更优. 最后,基于穆迪公司官方网站公布的2006年到2011年全球每年违约公司债券和贷款的违约回收率统计数据共653个数据,我们的实证案例分析表明,本文引入的边界核方法与现有普遍使用的以Beta分布刻画回收率的方法相比较,通过拟合优度检验和Bootstrap检验,我们的违约回收率密度函数模拟的非参数边界核方法比对应的Beta分布刻画方法更可靠,同时我们的结果也明显优于Beta分布刻画的回收率模型.     

A Superlinearly Convergent Combined PhaseⅠ-PhaseⅡ Subfeasible Method

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Generalized variation iteration solution of an atmosphere-ocean oscillator model for global climate

A box model of the interhemispheric thermohaline circulation (THC) in atmosphere-ocean for global climate is considered. By using the generalized variational iteration method, the approximate solution of a simplified nonlinear model is studied. The generalized variational iteration method is an analytic method, and the obtained analytic solution can be operated sequentially. The authors also diversify qualitative and quantitative behaviors for corresponding physical quantities.     

二阶积-微分方程奇异边值问题解的存在性

讨论了一类二阶积 微分方程两点边值问题解的存在性。该问题以四阶微分方程两点边值问题为特例。首先在不假设非线性项单调,并允许其有奇性的情况下,利用上下解方法与Schauder不动点定理,获得了二阶Fredholm型积 微分方程两点边值问题解的存在性结果,然后把该结果应用于两端简单支撑的弹性梁的平衡状态模型—四阶微分方程边值问题。     

裂缝波导阵天线设计计算的一些处理

本文对裂缝波导阵天线设计计算进行综述,提出一些处理。为了避免计算裂缝之间互耦系数的大量数值积分时间,给出泰勒级数展开和直接插值方法。在求解Elliott设计程序中出现的非线性方程组时,应用了逐次消元迭代方法。所有这些处理使计算时间大量减少。     

COMPARISON OF MAX—MIN APPROACH AND NN METHOD FOR RELIABILITY OPTIMIZATION OF SERIES—PARALLEL SYSTEM

Two heuristics, the max-min approach and the Nakagawa and Nakashima method, are consideredfor the redundancy allocation problem with series-parallel structure. The max-min approach canformulate the problem as an integer linear programming problem instead of an integer nonlinearproblem. This paper presents a comparison between those methods from the standpoint of solutionquality and computational complexity. The experimental results show that the max-min approach issuperior to the Nakagawa and Nakashima method in terms of solution quality in small-scale problems,but analysis of computational complexity shows that the max-min approach is inferior to other greedyheuristics.     

基于UKF的低成本SINS/GPS组合导航系统滤波算法

针对MIMU的精度不高,会带来较大的初始对准误差角,如果继续采用传统的小干扰线性方程就会给滤波带来很大误差,甚至发散。针对这个问题,对低成本SINS/GPS组合导航系统建立了基于四元数误差模型的非线性滤波方程,并采用了UKF非线性滤波方法。针对四元数误差模型单纯使用UKF方法无法估计加计零偏和陀螺漂移的问题,提出将UKF和EKF相结合的算法,仿真结果表明,比起扩展卡尔曼滤波以及采用传统小干扰线性方程的卡尔曼滤波,这种方法能够提高姿态误差角特别是方位误差角的估计精度。     

等式约束的凸非线性规划问题降维算法

对等式约束的凸非线性规划问题的非线性方程组算法进行了研究.从一般等式约束问题的最优性条件出发,构造一个非线性方程组,解此方程组便可求得非线性规划问题的最优解.     

Global convergence of a class of smooth penalty methods for semi-infinite programming

For the semi-infinite programming (SIP) problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.     

分解刚性大系统数值仿真并行算法

针对一类分解的刚性大系统，根据系统分割的思想，提出了组合ＲＫ－Ｒｏｓｅｎｂｒｏｃｋ方法，将方法分割和系统分割的思想相结合，构造了并行组合方法。对于提出的并行算法，比较系统地研究了算法的构造以及它们的收敛性和数值稳定性，并在微机和多处理机上进行了数值仿真试验。     

A characteristic set method for solving boolean equations and applications in cryptanalysis of stream ciphers*

This paper presents a characteristic more efficient and has better properties than the set method for solving Boolean equations, which is general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.     

Preconditioned method in parallel computation

1.INTRODUCTIONDecreasing the ti mes of communication andincreasingthe rate of it in the whole domain is very i mportantfor i mproving the rate of parallel computation in de-composed domain.Preconditioned technology hasbeen used widelyin this area[1]because it can changethe mode of communication andi mprove the topologi-cal configuration.Orthogonalization is a perfect pre-conditionedtechnology,but it isi mpossibleto orthog-onalize entirely for the large workload of computationand effect of …     

中国外债最优结构研究:人工神经网络方法

通过将BP神经网络和非线性方程组求解结合起来，提出了一种求解一般抽象非线性方程组F（x^-,y^-）=O的算法，并将其应用于中国宏观外债模型，样本检验结果指出，有92%的变量相对误差小于5%，该结果优于一般计量经济学方法所得的结果，应用该模型对中国外债管理方式（计划管理方式和余额管理方式）和期限结构进行仿真研究，研究结果在适度外债规模和外债管理方式及其在对国民经济的影响等方面提出了有较大政策参考价值的建议，说明了人工神经网络方法在复杂经济系统方面的应用前景。     

一个新自治混沌系统的动力学分析

提出了一个新的三维连续自治混沌系统.该系统含有4个控制参数,2个不同的非线性乘积项,并且方程式中含有指数形式的非线性项e(dz).利用理论推导、数值仿真对系统的基本动力学特性进行了分析,通过分岔图、Lyapunov指数图、Poincaré映射和相图等分析了控制参数变化时,系统动力学行为的变化.结果表明该新系统不但和Lorenz系统族有类似的性质,而且又呈现不同的非线性特征.     

非线性微分代数方程的一种离散波形松弛算法

讨论用迭代方法求解微分代数方程。针对一类非线性微分代数方程连续时间波形松弛迭代格式,应用一般的单支方法和线性多步法,得到离散时间波形松弛迭代格式。在假定分裂函数满足Lipschitz条件的前提下,通过矩阵正则分裂和特殊矩阵相关性质的运用,获得离散波形松弛迭代的收敛性条件,拓展和改进了相关文献中的一些结果。     

一种新的SHEPWM三电平逆变系统的仿真和实验研究

针对中点钳位型三电平逆变系统SHEPWM开关角度的求解问题,提出了基于混沌蚁群算法的三电平中点钳位型逆变系统的SHEPWM优化方法.蚁群算法在求解SHEPWM非线性超越方程组时不需要求解方程特定的初值,而变尺度混沌算子融合到蚁群算法之中,可以有效防止算法陷入局部最优解,提高计算精度.仿真和实验结果证明了基于混沌蚁群算法的三电平NPC逆变系统消谐模型的有效性.     

Study on Variation of Parameters Formula and Stability for Impulsive Time－Delay Nonlinear Large Scale Systems

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