高阶非线性微分方程的并行演化建模算法

文章提出了动态数据的高阶非线性微分方程的并行演化建模算法。动态系统的传统模型多采用线性模型,不能充分描述复杂系统的动态行为,建立高阶非线性微分方程模型更具普遍意义。我们通过将建模过程分解为可以分布并行的、模型结构选择和“模型参数优化”二个步骤,在异构网络环境中用CORBA实现了高阶微分方程建模的并行演化算法。实验表明,新的并行演化算法对于复杂动态系统的建模是十分有效的。     

一种用于合成光纤布拉格光栅的全时域算法

基于离散的光纤布拉格光栅(FBG)模型,推导了时域内的传输矩阵和散射矩阵;根据因果分析,提出了一种全时域的FBG合成算法,它能直接在时域内计算已知FBG的冲激响应.这种算法在迭代求解的过程中仅使用了简单的变换和移位操作,并考虑了光在FBG中多个反射点间的来回反射,能适用于高反射率FBG的重构.FBG合成的数值模拟,证实了这种全时域算法的优越性.     

MLSSM算法实现网格离散复杂目标的优化设计

为改进三维大尺寸复杂物体电磁建模精确求解的效率,采用了自适应交叉算法(ACA)基础上的多层简易矩阵稀疏算法(MLSSM)改进的方式,通过算法的理论及实现过程分析在实验验证中表明:应用的改进ACA算法计算效率比矩量法逐点计算显著提高;改进的MLSSM的内存需求减少了一半左右,矩阵构造过程速度有了明显提高;改进的MLSSM降低了计算复杂度,迭代求解过程速度有了明显提高。从算法对比结果可以看出,改进的MLSSM在降低计算复杂度方面占据优势,在分析半空间上大目标复杂物体优势明显。这一研究对复杂物体的电磁建模优化具有一定的理论和应用意义。     

联合稀疏信号恢复的贪婪增强贝叶斯算法

本文针对联合稀疏信号恢复问题,提出了一种贪婪增强贝叶斯算法.算法首先利用联合稀疏的特点对信号进行建模,然后在贝叶斯框架下,提出一种贪婪推理方式对信号恢复问题进行迭代求解.在迭代过程中,提出算法利用贝叶斯估计的方差信息来增强支撑恢复的结果,极大地提高了算法对信号恢复性能.理论分析表明:提出算法与同步正交匹配追踪算法具有相同的计算复杂度,远低于其他联合稀疏信号恢复算法.提出方法在具有高恢复精度和较低计算复杂度的同时,兼具贝叶斯方法和贪婪算法的优点.数值仿真验证了理论分析的有效性.     

一种有多反射特性的超宽带信道建模方法

在几何单反射椭圆信道模型和几何随机信道模型基础上,针对电磁波传播过程中出现的多反射特性,提出一种多反射特性的无线信道建模方法。把该方法应用于超宽带信道研究,可以得到UWB信道的几何随机多反射模型(GSMB)。使用该方法对两个UWB信号传播环境进行仿真分析,仿真得到的UWB信道功率延迟分布与实验结果基本一致,同时也验证了其他研究者关于UWB信道中的成簇现象具有确定性的结论。     

马氏调节反射O-U过程的平稳分布

讨论了一类特殊随机过程,即马氏调节双边反射带跳的O-U过程。其中的参数和跳均被一个有限状态空间、连续时间的齐次不可约马氏链所调节。文中的主要目的是证明该过程的平稳分布满足一个交互积分-微分方程。尤其当,马氏链只有两个状态时,讨论交互积分-微分方程解的存在唯一性问题,并在给出合适的边界条件下进行数值说明。     

计算机科学中几个算法及建模应用的探究

模型是将实际问题数学化,算法是将其中所蕴含的数学问题进行求解.算法即计算方法,是求解数学模型用的,就是将模型解出的方法.计算机科学中算法的选择、应用好坏,对建模具有非常重要的意义.本文简要论述了计算机科学中几个算法及建模应用具体内容,仅供交流.     

用Matlab进行插值法比较教学研究

插值方法是"数值分析"课程中非常重要的教学内容,也是数值微分、数值积分和常微分方程初值问题数值解的基础。本文探讨了插值问题的基本思想和常用的几种插值方法,重点比较了代数多项式插值方法。利用Matlab在科学计算中的优势,在实践教学中用Matlab进行了插值方法的对比教学研究。结果表明:通过比较教学使学生较快掌握了插值算法知识点,并能应用于实际科学研究项目之中,取得了较好的教学效果。     

基于多层简易矩阵稀疏算法的复杂物体建模优化的研究

为了提高三维大尺寸复杂物体电磁建模的精确求解的效率,改进了自适应交叉算法(ACA)基础上的多层简易矩阵稀疏算法(MLSSM),通过对算法的理论及实现过程分析,并在实验验证中表明:应用的改进ACA算法计算效率比矩量法逐点计算显著提高;改进的MLSSM的内存需求减少了1 2左右,矩阵构造过程速度有了明显提高;改进的MLSSM降低了计算复杂度,迭代求解过程速度有了明显提高。算法对比结果看出改进的MLSSM在降低计算复杂度方面占据的优势,在分析半空间上大目标复杂物体优势明显。这一研究对于复杂物体的电磁建模的优化有一定的理论和应用意义。     

代数迭代法在激光反射断层成像目标重构中的应用

为了提高激光反射断层成像目标重构的图像质量,在目前激光反射断层成像普遍采用反投影算法重构图像的基础上,将CT成像中常用的迭代重建算法引入到激光反射断层成像的图像重构过程中。分析了反投影算法中的直接反投影、R-L和S-L滤波反投影以及迭代重建算法在图像重构中的性能特性。进行了仿真和外场实验,结果表明:在直接反投影基础上添加了滤波器的反投影算法在减小误差和抑噪能力上都明显提高;另外相比于反投影算法,代数迭代重建算法表现出更好的重建质量,且具有更强的抑噪性能。     

Weak convergence and local stability properties of fixed step sizerecursive algorithms

A recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation (ODE). The ODEs describing the motion of several common adaptive filters are examined in some simple settings, including the least mean square (LMS) algorithm and all three of its signed variants (the signed regressor, the signed error, and the sign-sign algorithms). Stability and instability results are presented in terms of the eigenvalues of a correlation-like matrix. This generalizes known results for LMS, signed regressor LMS, and signed error LMS, and gives new stability criteria for the sign-sign algorithm. The ability of the algorithms to track moving parameterizations can be analyzed in a similar manner, by relating the time varying system to a forced ODE. The asymptotic distribution about the forced ODE is an Ornstein-Uhlenbeck process, the properties of which can be described in a straightforward manner     

An Alternative Algorithm for Both Narrowband and Wideband Lorentzian Dispersive Materials Modeling in the Finite-Difference Time-Domain Method

In this study, an alternative algorithm is proposed for modeling narrowband and wideband Lorentzian dispersive materials using the finite-difference time-domain (FDTD) method. Previous algorithms for modeling narrowband and wideband Lorentzian dispersive materials using the FDTD method have been based on a recursive convolution technique. They present two different and independent algorithms for the modeling of the narrowband and wideband Lorentzian dispersive materials, known as the narrowband and wideband Lorentzian recursive convolution algorithms, respectively. The proposed alternative algorithm may be used as a general algorithm for both narrowband and wideband Lorentzian dispersive materials modeling with the FDTD method. The second-order motion equation for the Lorentzian materials is employed as an auxilary differential equation. The proposed auxiliary differential-equation-based algorithm can also be applied to solve the borderline case dispersive electromagnetic problems in the FDTD method. In contrast, the narrowband and wideband Lorentzian recursive convolution algorithms cannot be used for the borderline case. A rectangular cavity, which is partially filled with narrowband and wideband Lorentzian dispersive materials, is presented as a numerical example. The time response of the electric field z component is used to validate and compare the results     

On the statistics of the error in predictive coding for stationaryOrnstein-Uhlenbeck processes

Explicit expression are derived for the conditional expectation and variance of the encoder in a predictive DPCM coder with an N-level quantizer, when a stationary Ornstein-Uhlenbeck process is a source. A representation of the encoder in terms of a stochastic integral is presented. These expressions yield a nonlinear stochastic difference equation for the decoding error process and a stochastic differential equation (SDE) as a weak limit for the error process. The statistical properties of the error obtained as a solution of the limiting SDE are interpreted in terms of the slope overload error     

Instantaneous Frequency Estimation When the Amplitude is a Stochastic Process Using Stochastic Calculus and Bootstrapping

Stochastic calculus methods are used to estimate the frequencies of a polynomial sinusoid when the amplitude is modeled as an Ornstein-Uhlenbeck process. Using stochastic calculus, one is able to develop a stochastic differential equation that relates the observations to the frequencies. The likelihood function is obtained through Girsanov theory and the Radon-Nikodym derivative. Maximum likelihood estimates are obtained numerically using stochastic annealing. Bootstrapping is used to improve the estimate of the frequencies.     

受启发的人工蜂群算法在全局优化问题中的应用

 人工蜂群算法是最近提出的一种较有竞争力的优化技术.然而,它的搜索方程存在着探索能力强而开发能力弱的缺点.针对这一问题,受差分进化算法的启发,提出了一个改进的搜索方程.该搜索方程在最优解附近产生新的候选位置以便提高算法的开发能力.进一步,充分利用和平衡不同搜索方程的探索和开发能力,提出了一个改进的人工蜂群算法(简记为IABC).此外,为了提高算法的全局收敛速度,用反学习的初始化方法产生初始解.通过18个标准测试函数的仿真实验并与其他算法相比较,结果表明IABC算法具有良好的处理复杂数值优化问题的性能.     

前向神经网络的神经元分层逐个线性优化快速学习算法

本文提出了一种新的前向神经网络快速分层学习算法.在此学习算法中,其优化策略为对输出层和隐层神经元的连接权值交替优化.对输出层权值优化算法采用基于广义逆的最小二乘递推算法,对隐层神经元的连接权值采取则对每个神经元逐个进行优化,而且采用正交变换加快每一步学习的计算速度和提高算法的数值稳定性.当学习过程停滞时采用随机扰动的方法摆脱过早收敛.数值实验表明,与BP动量因子法、牛顿型方法和现有的分层优化算法相比,新算法不仅学习速度快学习时间短,而且当网络规模增大时仍然比较有效.     

Stochastic Differential Equations for Modeling of High Maneuvering Target Tracking

In this paper, we propose a new adaptive single model to track a maneuvering target with abrupt accelerations. We utilize the stochastic differential equation to model acceleration of a maneuvering target with stochastic volatility (SV). We assume the generalized autoregressive conditional heteroscedasticity (GARCH) process as the model for the tracking procedure of the SV. In the proposed scheme, to track a high maneuvering target, we modify the Kalman filtering by introducing a new GARCH model for estimating SV. The proposed tracking algorithm operates in both the non‐maneuvering and maneuvering modes, and, unlike the traditional decision‐based model, the maneuver detection procedure is eliminated. Furthermore, we stress that the improved performance using the GARCH acceleration model is due to properties inherent in GARCH modeling itself that comply with maneuvering target trajectory. Moreover, the computational complexity of this model is more efficient than that of traditional methods. Finally, the effectiveness and capabilities of our proposed strategy are demonstrated and validated through Monte Carlo simulation studies.     

基于随机微分方程模型的股票预测

金融时间序列是复杂的动态系统,是非线性、混沌和时变的[1],影响金融市场的因素众多,它们之间的相互作用复杂多变。为了更合理的解释经济运行的规律,本文提出了随机微分方程模型,该模型利用进化算法拟合时间序列数据,在常微分方程基础上加入随机项,模拟系统的运作。     

Adaptive Algorithm of Tracking the Best Experts Trajectory

The problem of decision theoretic online learning is discussed. There is the set of methods, experts, and algorithms capable of making solutions (or predictions) and suffering losses due to the inaccuracy of their solutions. An adaptive algorithm whereby expert solutions are aggregated and sustained losses not exceeding (to a certain quantity called a regret) those of the best combination of experts distributed over the prediction interval is proposed. The algorithm is constructed using the Fixed-Share method combined with the Ada-Hedge algorithm used to exponentially weight expert solutions. The regret of the proposed algorithm is estimated. In the context of the given approach, there are no any stochastic assumptions about an initial data source and the boundedness of losses. The results of numerical experiments concerning the mixing of expert solutions with the help of the proposed algorithm are presented. The strategies of games on financial markets, which were suggested in our previous papers, play the role of expert strategies.