A New Weight Initialization Method Using Cauchy’s Inequality Based on Sensitivity Analysis

In this paper, an efficient weight initialization method is proposed using Cauchy’s inequality based on sensitivity analy- sis to improve the convergence speed in single hidden layer feedforward neural networks. The proposed method ensures that the outputs of hidden neurons are in the active region which increases the rate of convergence. Also the weights are learned by minimizing the sum of squared errors and obtained by solving linear system of equations. The proposed method is simulated on various problems. In all the problems the number of epochs and time required for the proposed method is found to be minimum compared with other weight initialization methods.

ON THE MONOTONE CONVERGENCE OF THE PROJECTED ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.

Higher Order Aitken Extrapolation with Application to Converging and Diverging Gauss-Seidel Iterations

In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometric series sum is a known form of Aitken acceleration, it is shown that in this paper, the same formula can be used to estimate the solution of sets of linear equations from diverging Gauss-Seidel iterations. In both convergent and divergent iterations, the ratios of differences among the consecutive values of iteration eventually form a convergent (divergent) series with a factor equal to the largest Eigen value of the iteration matrix. Higher order Aitken extrapolation is shown to eliminate the influence of dominant Eigen values of the iteration matrix in successive order until the iteration is determined by the lowest possible Eigen values. For the convergent part of the Gauss-Seidel iteration, further acceleration is made possible by coupling of the extrapolation technique with the successive over relaxation (SOR) method. Application examples from both convergent and divergent iterations have been provided. Coupling of the extrapolation with the SOR technique is also illustrated for a steady state two dimensional heat flow problem which was solved using MATLAB programming.

On Minimization of Upper Bound for the Convergence Rate of the QHSS Iteration Method

For an upper bound of the spectral radius of the QHSS (quasi Hermitian and skew-Hermitian splitting) iteration matrix which can also bound the contraction factor of the QHSS iteration method,we give its minimum point under the conditions which guarantee that the upper bound is strictly less than one. This provides a good choice of the involved iteration parameters,so that the convergence rate of the QHSS iteration method can be significantly improved.

An Improved Double r-iteration IOD Method for GEO UCTs Based on SBSS System

The purpose of initial orbit determination,especially in the case of angles-only data for observation,is to obtain an initial estimate that is close enough to the true orbit to enable subsequent precision orbit determination processing to be successful.However,the classical angles-only initial orbit determination methods cannot deal with the observation data whose Earth-central angle is larger than 360°.In this paper,an improved double r-iteration initial orbit determination method to deal with the above case is presented to monitor geosynchronous Earth orbit objects for a spacebased surveillance system.Simulation results indicate that the improved double r-iteration method is feasible,and the accuracy of the obtained initial orbit meets the requirements of re-acquiring the object.

CONVERGENCE OF ITERATION METHODS OF MAXIMUM LIKELIHOOD ESTIMATOR AND ITS APPLICATIONS

Iteration methods and their convergences of the maximum likelihoodestimator are discussed in this paper.We study Gauss-Newton method and give a set ofsufficient conditions for the convergence of asymptotic numerical stability.The modifiedGauss-Newton method is also studied and the sufficient conditions of the convergence arepresented.Two numerical examples are given to illustrate our results.

Variational Iteration Method Solutions for Certain Thirteenth Order Ordinary Differential Equations

In this paper, we extend variational iteration method (VIM) to find approximate solutions of linear and nonlinear thirteenth order differential equations in boundary value problems. The method is based on boundary valued problems. Two numerical examples are presented for the numerical illustration of the method and their results are compared with those considered by [1,2]. The results reveal that VIM is very effective and highly promising in comparison with other numerical methods.

Probabilistic Approach to the Asynchronous Iteration

In this work we will consider asynchronous iteration algorithms. As is well known in multiprocessor computers the parallel application of iterative methods often shows poor scaling and less optimal parallel efficiency. The ordinary iterative asynchronous method often has much better parallel efficiency as they almost never need to wait to communicate between possessors. We will study probabilistic approach in asynchronous iteration algorithms and present a mathematical description of this computational process to the multiprocessor environment. The result of our simple numerical experiments shows a convergence and efficiency of asynchronous iterative processes for considered nonlinear problems.

On the Deepest Fallacy in the History of Mathematics: The Denial of the Postulate about the Approximation Nature of a Simple-Iteration Method and Iterative Derivation of Cramer’s Formulas

Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.

Efficient Orbit Propagation of Orbital Elements Using Modified Chebyshev Picard Iteration Method

This paper focuses on propagating perturbed two-body motion using orbital elements combined with a novel integration technique.While previous studies show that Modified Chebyshev Picard Iteration(MCPI)is a powerful tool used to propagate position and velocity,the present results show that using orbital elements to propagate the state vector reduces the number of MCPI iterations and nodes required,which is especially useful for reducing the computation time when including computationally-intensive calculations such as Spherical Harmonic gravity,and it also converges for>5.5x as many revolutions using a single segment when compared with cartesian propagation.Results for the Classical Orbital Elements and the Modified Equinoctial Orbital Elements(the latter provides singularity-free solutions)show that state propagation using these variables is inherently well-suited to the propagation method chosen.Additional benefits are achieved using a segmentation scheme,while future expansion to the two-point boundary value problem is expected to increase the domain of convergence compared with the cartesian case.MCPI is an iterative numerical method used to solve linear and nonlinear,ordinary differential equations(ODEs).It is a fusion of orthogonal Chebyshev function approximation with Picard iteration that approximates a long-arc trajectory at every iteration.Previous studies have shown that it outperforms the state of the practice numerical integrators of ODEs in a serial computing environment;since MCPI is inherently massively parallelizable,this capability is expected to increase the computational efficiency of the method presented.

A Novel Method to Enhance the Inversion Speed and Precision of the NMR T_(2) Spectrum by the TSVD Based Linearized Bregman Iteration

The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises.This paper proposes a novel inversion algorithmto accelerate the convergence and enhance the precision using empirical truncated singular value decompositions(TSVD)and the linearized Bregman iteration.The L1 penalty term is applied to construct the objective function,and then the linearized Bregman iteration is utilized to obtain fast convergence.To reduce the complexity of the computation,empirical TSVD is proposed to compress the kernel matrix and determine the appropriate truncated position.This novel inversion method is validated using numerical simulations.The results indicate that the proposed novel method is significantly efficient and can achieve quick and effective data solutions with low signal-to-noise ratios.

基于改进初值带遗忘因子的递推最小二乘法的锂电池参数辨识

锂电池荷电状态(state of charge,SOC)的准确估计依赖于精确的锂电池模型参数。在采用带遗忘因子的递推最小二乘法(forgetting factor recursive least square,FFRLS)对锂电池等效电路模型进行参数辨识时,迭代初始值选取不当会造成辨识精度低、收敛速度慢的问题。为此,将电路分析法与FFRLS相结合,提出基于改进初值带遗忘因子的递推最小二乘法(improved initial value-FFRLS,IIV-FFRLS)。首先,通过离线辨识得到各荷电状态点对应的等效电路模型参数并进行多项式拟合;然后,利用初始开路电压(open circuit voltage,OCV)和OCV-SOC曲线获得初始SOC,代入参数拟合函数得到初始参数;最后,将初始参数带入递推公式得到IIV-FFRLS迭代初始值。对4种锂电池工况进行参数辨识,结果表明:与传统方法相比,IIV-FFRLS的平均相对误差、收敛时间分别减小58%、23%以上;IIV-FFRLS具有更高的辨识精度与更快的收敛速度。

基于主题词向量中心点的K-means文本聚类算法

K-means由于其时间复杂度低运行速度快一直是最为流行的聚类算法之一,但是该算法在进行聚类时需要预先给出聚类个数和初始类中心点,其选取得合适与否会直接影响最终聚类效果。该文对初始类中心和迭代类中心的选取进行大量研究,根据决策图进行初始类中心的选择,利用每个类簇的主题词向量替代均值作为迭代类中心。实验表明,该文的初始点选取方法能够准确地选取初始点,且利用主题词向量作为迭代类中心能够很好地避免噪声点和噪声特征的影响,很大程度上地提高了K-means算法的性能。

全状态约束下长行程混联机器人投影迭代鲁棒控制算法

针对全状态约束下的长行程混联机器人系统鲁棒性较差提出了基于自适应学习神经网络和等效误差函数的投影迭代鲁棒控制算法。基于自适应学习神经网络逼近未知的非线性项,提出投影迭代鲁棒控制算法,更新网络权值并估计逼近误差和随机外部扰动的未知上界;构造用于抵消初始时刻随机变化扩展误差的时变边界层,设计基于时变边界层和扩展误差的等效误差函数作为迭代控制器的主要控制变量以克服随机初始误差满足相同初始条件;在控制器设计中引入正切型障碍Lyapunov函数,确保系统状态在预定范围内。仿真实验结果证明了该方法的有效性,可在全状态约束下实现高精度强鲁棒性的轨迹跟踪。

基于超像素快速模糊聚类的印刷品图像分割方法

针对当前彩色印刷品色差检测过程中效率低、复杂性高等问题,提出了一种基于超像素快速模糊聚类的印刷品图像分割方法(SFFCM)。先用简单线性迭代聚类(SLIC)算法将图像分割为紧密相邻的超像素区域。每个超像素区域被视为一个独立的聚类单元。随后,将模糊C均值聚类(FCM)算法应用于超像素的归属关系计算中,即引入隶属度值,允许超像素归属于多个聚类中心,并通过权衡归属度值来实现模糊聚类。实验结果表明,相对于其他算法,本文方法在保持良好实时性的同时,实现了较好的分割效果,有效平衡了算法复杂度与分割效果之间的关系。

双通道深度图像先验降噪模型

相对于采用固定网络参数值的有监督深度降噪模型而言,无监督的深度图像先验(Deep Image Prior,DIP)降噪模型更具灵活性和实用性.然而,DIP模型的降噪效果远低于有监督降噪模型(尤其是在处理人工合成噪声图像时).为进一步提升DIP降噪模型的降噪效果,本文提出了双通道深度图像先验降噪模型.该降噪模型由噪声图像预处理、在线迭代训练和图像融合3个模块组成.首先,利用BM3D和FFDNet两种经典降噪方法对给定的噪声图像进行预处理,得到2张初步降噪图像,然后,将原DIP单通道逼近目标图像架构拓展为双通道工作模式.其中,第一通道以FFDNet初步降噪图像和噪声图像为双目标图像,第二通道则以BM3D预处理图像和噪声图像为双目标图像.在此基础上,按照标准的DIP在线训练方式让DIP网络输出图像在两个通道上分别逼近各自的目标图像,同时依据基于边缘能量定义的伪有参考图像质量评价值适时终止迭代过程,从而获得2张中间生成图像.最后,使用结构化图块分解融合算法将两张中间生成图像融合并作为最终的降噪后图像.实验数据表明,在合成噪声图像上,本文提出的双通道深度图像先验降噪模型在各个噪声水平上显著优于原DIP及其他无监督降噪模型(提升了约2.2 dB),甚至逼近和超过了新近提出的主流有监督降噪模型,这充分表明了本文提出的改进策略的有效性;在真实噪声图像上,本文提出的降噪模型优于排名第二的对比降噪方法约2 dB,展现出其在实际应用场景下独有的优势.

基于自适应终端滑模的高速列车迭代学习速度控制

针对高速列车的速度追踪控制问题,充分利用列车运行的重复性,考虑工程应用中迭代初始状态不同和复杂的外部环境,提出一种基于线性扩张状态观测器(LESO)的自适应非奇异终端滑模迭代学习控制算法,使系统在任意迭代初值时均能保证追踪精度。提出一种时变非奇异终端滑模面以抑制初态误差影响,采用LESO估计并补偿列车扰动,设计自适应迭代更新律估计LESO的观测误差,设计全饱和自适应迭代控制律计算输入并将其约束于允许范围内。建立类Lyapunov的复合能量函数,通过严格的数学分析证明其迭代域的差分负定性和有界性,证明所设计的时变滑模面可实现渐进收敛,并证明追踪误差在滑模面内可在有限时间内收敛至平衡点。将本文提出的算法与滑模控制、变增益迭代学习控制、自抗扰控制等算法进行比较。仿真结果表明:无论是否存在迭代初始误差,在相同的条件下,本文提出的算法较其他算法具有更强的抗干扰能力,速度追踪精度提高90%及以上,停车误差可迭代收敛至001 m。

非线性方程牛顿迭代法的三点注记

针对求解非线性方程的牛顿迭代法做了三点注记:①对某些方程,任意初始值牛顿迭代法均收敛;②对某些方程,在某一区间上取初始值,牛顿迭代法不收敛;③对某些方程,迭代值交替出现,牛顿迭代法不收敛。

基于回归算法的MARK Ⅲ薄膜型LNG运输船结构分析优化

针对国内首艘MARK Ⅲ薄膜型LNG运输船(LNG JUMBO)货舱区的结构设计,采用挪威船级社(DNV)开发的Nauticus Hull和Sesam软件完成舱段结构有限元分析。通过对目标舱加载的计算,校核舱内各主要构件的屈服、屈曲强度;基于子模型技术,评估各关键区域高应力点结构强度,并提出一种高效推算同一位置、不同强框处应力值的线性迭代回归算法,为结构优化与产品轻量化提供了新思路。

初始大扰动条件下双流系统的粒子相空间振荡

双流系统产生的不稳定性过程是近地空间中常见的等离子体不稳定性现象.地球磁尾、等离子体片边界层、地球弓激波、太阳风、极隙区和极光加速区观测到的静电孤立波被认为是由双流不稳定性产生.地球空间环境并非均匀稳态,因此对双流系统演化过程的研究往往需要考虑初始的扰动.利用所建立的动理论粒子云模型方法,我们研究了初始大扰动下双流系统的不稳定性现象,发现初始大扰动条件下粒子相空间产生振荡现象,且振荡频率与初始扰动的空间波数有关,电场与电场能量也存在该频率成分.通过线性理论,求解出了粒子相空间振荡频率.它与粒子云模拟得到的频率一致.该频率为朗缪尔振荡频率的基础之上叠加一个与初始扰动的空间波数有关的频率偏移量.我们改变等离子体频率,进一步验证了上述结论.该研究结果表明初始扰动能够对双流系统的不稳定性现象产生重要影响,对于加深理解地球磁层中双流系统的演化过程有重要参考意义.