一种超松弛原始对偶不动点算法及其应用

近年来,关于两个凸函数和的优化问题受到极大关注,其中一凸函数可微且其梯度满足 Lipschitz 连续性,另一凸函数包含有界线性算子。提出一种超松弛原始对偶不动点算法求解这一类问题,相比于原始对偶不动点算法,所提算法扩展了松弛参数的选择范围。通过定义合适的范数,运用非扩张算子不动点理论,证明所提迭代算法的收敛性,并证明算法的遍历收敛率。在对目标函数一些强的条件下,证明算法具有全局线性收敛率。最后,为验证算法的有效性和优越性,将所提算法运用于求解全变分图像复原模型,数值结果表明,选择松弛参数大于 $1$ (即超松弛) 的原始对偶不动点算法比松弛参数小于 $1$ 时算法收敛更快。     

一类非线性算子方程的迭代求解

本文利用锥理论研究一类非线性算子方程 x=Ax (1)的迭代求解的问题,在本文中,我们对算子A的连续性和紧性,没有做任何假定,但是我们证明了在某些条件下,本文所给出的迭代序列{x_n},依范数收敛于方程(1)的解,并给出了收敛速度的估计。     

α-β广义逆的迭代法

广义逆的性质在数值分析与数理统计等领域中有着非常重要的作用,而迭代方法在求解广义逆的实际问题中是一种非常有效的方法.本文主要利用矩阵α-β广义逆的相关性质,给出了α-β广义逆的四种迭代格式,并研究每种迭代格式收敛的充分必要条件.同时利用Frobenius范数给出了迭代收敛的误差界.最后给出数值算例,表明本文所提出的迭代...     

求解互补问题的原始对偶起作用集算法

在本文中我们得到了求解带T-单调算子的互补问题的原始对偶活跃集算法的收敛结果.当原始对偶活跃集算法求解此类互补问题时,此算法可以作为一类特殊的半光滑牛顿法.收敛结果和数值试验说明了此算法的迭代次数不超过问题未知数的个数.最终,计算结果表明此算法的可行性.     

人工神经网络在建筑物物理力学参数识别中的应用

基于神经网络的BP算法,建立了识别建筑物物理力学参数的数值方法.在经典的BP算法中,网络中的权值的确定是将权值的计算修正过程描述为网络的训练过程,其中迭代步长由经验选定,常常造成收敛速度慢,并且收敛速度与初始权值的选择有关以及引起振荡等问题.在网络的训练过程中采用改进的BP算法,通过对学习算子的优化搜索,大大提高了网络的收敛速度,解决了BP算法迭代过程中目标函数的震荡问题.数值计算表明,所提出的改进的BP算法进行建筑结构物理力学参数识别的收敛速度和识别精度都得到了提高.     

线性离散时不变系统的共轭方向优化迭代学习控制

本文针对一类线性离散时不变系统,利用共轭方向优化方法设计了一种迭代学习控制算法.首先,基于采样数据构建超向量,将原二维动态系统转化为迭代域中的一维系统.其次,在这种形式下,利用当前的跟踪误向量减去其在以前搜索方向上的投影,构建新的搜索方向,以补偿当前的控制信号,进而构建下一次迭代的控制信号.再次,结合共轭方向的性质,利用数学归纳法分析了算法的单调收敛性和二次终止性.最后,数值仿真验证了理论分析的正确性和有效性;同时,与已发表的比例型和范数最优迭代学习控制方法进行比较,得出了本算法的优越性.     

线性离散时不变系统的共轭方向优化迭代学习控制（英文）

本文针对一类线性离散时不变系统,利用共轭方向优化方法设计了一种迭代学习控制算法.首先,基于采样数据构建超向量,将原二维动态系统转化为迭代域中的一维系统.其次,在这种形式下,利用当前的跟踪误向量减去其在以前搜索方向上的投影,构建新的搜索方向,以补偿当前的控制信号,进而构建下一次迭代的控制信号.再次,结合共轭方向的性质,利用数学归纳法分析了算法的单调收敛性和二次终止性.最后,数值仿真验证了理论分析的正确性和有效性;同时,与已发表的比例型和范数最优迭代学习控制方法进行比较,得出了本算法的优越性.     

一种新型快速收敛的LMS谐波检测算法

针对传统基于固定步长LMS算法在电网谐波检测中存在收敛速度与稳态精度需折中选择的问题,提出了一种新型具有较高收敛速度的改进变步长LMS算法。该算法以同一相位下相邻两时刻的误差信号e(n)、e(n－1)的自相关估计调节步长更新,并且采用归一化处理方式,以误差信号在总电流信号中的比例k(n)、k(n－1)作为新反馈量,同时对新的反馈量进行相干平均估计来调整步长迭代;在权值迭代公式中引入相邻时刻估计误差绝对值之差的扰动量来加快自适应滤波器权矢量的迭代速度。MATLAB/Simulink仿真和实验证明,该方法相对于传统固定步长LMS谐波检测算法在收敛速度和稳态精度上有了进一步的提高,尤其在负载发生突变时的跟踪能力。     

稀疏多径信道自适应均衡算法研究

针对传统自适应均衡算法在稀疏多径信道中性能较差的问题,提出了一种基于l₂-范数的自适应均衡算法。该算法利用稀疏多径信道下均衡器权值的稀疏性,将自适应均衡器的训练过程看作压缩感知理论中稀疏信号对字典的加权求和,以解决迭代参数的设置及收敛速度慢的问题。该算法将l₂-范数和压缩感知相结合,不仅提高了权值的精度,而且降低了计算复杂度。仿真结果表明,该算法计算量小,训练序列少,具有较好的性能,对提高系统的通信性能具有参考价值。     

求解鞍点问题的多项式加速超松弛方法

为了快速有效地求解大型稀疏鞍点问题,在广义逐次超松弛(GSOR)迭代算法的基础上,结合Chebyshev多项式加速技术,本文构造了一种多项式加速超松弛迭代算法,并研究了该算法的收敛性.通过讨论加速后迭代矩阵的收敛性证明了新方法比加速前的迭代法具有快的收敛速度.数值例子也表明新方法提高了GSOR算法的收敛效率.     

Multilevel Circulant Preconditioner for High-Dimensional Fractional Diffusion Equations

High-dimensional two-sided space fractional diffusion equations with variable diffusion coefficients are discussed. The problems can be solved by an implicit finite difference scheme that is proven to be uniquely solvable, unconditionally stable and first-order convergent in the infinity norm. A nonsingular multilevel circulant preconditoner is proposed to accelerate the convergence rate of the Krylov subspace linear system solver efficiently. The preconditoned matrix for fast convergence is a sum of the identity matrix, a matrix with small norm, and a matrix with low rank under certain conditions. Moreover, the preconditioner is practical, with an O(N logN) operation cost and O(N) memory requirement. Illustrative numerical examples are also presented.     

基于FxKalman算法的有源控制器设计与实现研究

近年来,对于有源噪声控制算法的性能越来越重视。与基于维纳滤波原理的最小均方滤波(Filtered-x Least Mean Square,Fx LMS)、最小二乘滤波(Filtered-x Recursive Least Square,Fx RLS)算法相比较,基于卡尔曼滤波的有源控制算法(Filtered-x Kalman,Fx Kalman)具有较快的收敛速度和良好的跟踪性能,且对带宽噪声有较好的降噪性能。设计、仿真运行了Fx Kalman算法的有源控制器,并针对单频、窄带和宽带信号,在实验室封闭空间对Fx Kalman算法、Fx LMS算法和Fx RLS算法进行有源控制器验证性实验比较,证实了Fx Kalman有源控制器具有上述优点。而如果初级噪声为单频信号且对算法收敛速度要求不高,Fx LMS算法是最经济稳妥的选择。当需要控制带宽噪声或对算法收敛速度要求较高时,Fx Kalman算法则为最好的选择。     

基于SCAD的压缩感知阈值迭代算法的收敛性分析

基于SCAD罚函数的压缩感知在有噪声稀疏信号重建中具有优良的理论及应用效果,开展其快速重建算法研究有着重要的意义,阈值迭代算法是解决压缩传感问题最有效的算法之一.本文研究了基于SCAD罚函数的压缩感知阈值迭代算法的收敛性问题,给出了算法收敛到稀疏解的充分条件,并证明了迭代估计值以指数阶速率收敛于最优值.进一步,本文给出了基于AMP改进的SCAD阈值迭代算法的收敛性分析.     

Drilling path optimization by the particle swarm optimization algorithm with global convergence characteristics

Drilling path optimization is one of the key problems in holes-machining. This paper presents a new approach to solve the drilling path optimization problem belonging to discrete space, based on the particle swarm optimization (PSO) algorithm. Since the standard PSO algorithm is not guaranteed to be global convergent or local convergent, based on the mathematical model, the algorithm is improved by adopting the method to generate the stop evolution particle once again to obtain the ability of convergence on the global optimization solution. Also, the operators are proposed by establishing the Order Exchange Unit (OEU) and the Order Exchange List (OEL) to satisfy the need of integer coding in drilling path optimization. The experimentations indicate that the improved algorithm has the characteristics of easy realization, fast convergence speed, and better global convergence capability. Hence the new PSO can play a role in solving the problem of drilling path optimization.     

Three-dimensional reconstruction of dielectric objects by the coupled-dipole method

We present an inversion procedure for electromagnetic scattering, based on the powerful and flexible technique called the coupled-dipole method combined with an optimization algorithm. This method permits us to realize imaging of dielectric objects whose dimensions are comparable with the incident wavelength and is shown to be efficient with corrupted data (scattered electric field). The feasibility of this method is shown in a synthetic example in which the scattered field is corrupted with Gaussian noise. Two methods are used to invert the scattered field to recover the refractive index of the medium: a conventional matrix inversion and an iterative method.     

Comparison of Dynamic Differential Evolution and Self-Adaptive Dynamic Differential Evolution for Buried Metallic Cylinder

The application of two techniques for the reconstruction of shape reconstruction of a metallic cylinder from scattered field measurements is studied in this paper. These techniques are applied to two-dimensional configurations, for which the method of moment (MoM) is applied to solve the integral equations. Considering that the microwave imaging is recast as a nonlinear optimization problem, an objective function is defined by the norm of the difference between the measured scattered electric fields and those calculated for each estimated metallic cylinder. Thus, the shape of a metallic cylinder can be obtained by minimizing the objective function. In order to solve this inverse scattering problem, two techniques are employed. The first one is based on dynamic differential evolution (DDE) algorithm, while the second one is an improved version of the DDE algorithm with self-adaptive control parameters, called SADDE. Both techniques are tested for the simulated data contaminated by additive white Gaussian noise. Numerical results indicate that SADDE algorithm outperforms DDE algorithm in terms of reconstruction accuracy and convergence speed.     

Necessary convergence conditions for upwind schemes in the two-dimensional case

This paper considers nine-point difference schemes for a two-dimensional boundary value singular perturbation problem without turning points and parabolic boundary layers. Necessary conditions are given for the uniform convergence (in the sense of the maximum norm) of a scheme. Using these conditions, several widely used schemes are analysed. It is shown that some common schemes are not uniformly convergent in ?. and that in some cases we are able to compute uniquely free parameters in the scheme. Some remarks on the treatment of a problem with a parabolic boundary layer are given.     

一种浅海水声信道分数间隔自适应均衡算法研究

水声信道是最为复杂的数据通信环境之一,而具有重要军用和商用价值的浅海水声信道,其多径与频散效应更为严重。在浅海水声数字通信中,普遍存在着码间干扰和码内干扰效应,严重影响了水下通信的速度和质量。在判决反馈结构的基础上,采用分数的方法,提出了一种适用于浅海水声信道的自适应均衡算法,并通过计算机仿真实验与整数方法进行了性能对比。传输信号采用正交相移键控调制方式,以有效利用有限通信带宽。仿真结果表明,该算法获得了较快的收敛速度和较小的稳态误差,提高了水声通信的有效性及可靠性,因而具有良好的工程应用价值。     

A novel learning-based switching median filter for suppression of impulse noise in highly corrupted colour images

A novel switching median filter integrated with a learning-based noise detection method is proposed for suppression of impulse noise in highly corrupted colour images. Noise detection employs a new machine learning algorithm, called margin setting (MS), to detect noise pixels. MS detection is achieved by classifying noise and clean pixels with a decision surface. MS detection yields very high detection accuracy, i.e. a zero miss detection rate and a fairly low over detection rate for a wide range of noise levels. After noise detection, a new filter scheme called the noise-free two-stage (NFTS) filter is triggered. NFTS corrects the noise pixels using the median of the noise-free pixels in two stages. The results of experiments have demonstrated that the MS based NFTS (MSN) filter is superior to the support vector machine and neural network for denoising highly corrupted images, in terms of noise suppression and detail preservation.     

An Optimal Multi-Vector Iterative Algorithm in a Krylov Subspace for Solving the Ill-Posed Linear Inverse Problems

An optimal m-vector descent iterative algorithm in a Krylov subspace is developed, of which the m weighting parameters are optimized from a properly defined objective function to accelerate the convergence rate in solving an ill-posed linear problem. The optimal multi-vector iterative algorithm (OMVIA) is convergent fast and accurate, which is verified by numerical tests of several linear inverse problems, including the backward heat conduction problem, the heat source identification problem, the inverse Cauchy problem, and the external force recovery problem. Because the OMVIA has a good filtering effect, the numerical results recovered are quite smooth with small error, even under a large noise up to 10%.