求解二维粒子输运方程的CGS算法

本文采用CGS算法来求解二维粒子输运方程。首先通过离散纵标法将输运方程离散为线性方程组的形式,同时引进预条件矩阵来改善系数矩阵的谱性质。通过数值试验,将预处理后的CGS算法与传统的源迭代方法进行对比,并对预处理前后特征值的分布做了比较。结果表明预处理后的矩阵特征值分布较为集中,且CGS算法收敛速度较快。     

n阶Fredholm积分-微分方程的有理Haar小波解法

一阶积分-微分方程是我们求解积分微分方程时常见的一类方程,其求解方法比较简单;而在实际问题中我们常常会遇到高阶积分-微分方程的求解,求其数值解相对比较困难。作者利用有理Haar小波的积分法和积分算子矩阵对一般的n阶Fredholm积分-微分方程进行了求解。最后给出的数值算例表明了该方法的有效性。     

“二维LP问题的一个直接算法”中定理反例

针对"二维LP问题的一个直接算法"一文中的算法基本定理,给出了两个反例,分别说明其中的引理和定理都是错误的,建立在这些结论基础上的求解一般线性规划问题的代数算法无法求出一般线性规划问题的最优解。数值试验表明,随着方程个数的增加,用他们的方法求得正确解的概率将越来越低。给出了一个二维线性规划问题最优解的性质定理,由该定理可导出文[1]中代数算法有效的条件。     

矩阵方程的变换解法

本文针对求解矩阵方程的问题,提出了三种不同层次的解法。尤其对利用初等变换解矩阵方程的方法,进行了详细的分析。     

求解指派问题的新方法

本文针对求解指派问题的匈牙利算法中的独立零元素,提出了闭回路矩阵和纯伪零点的概念.通过对纯伪零点性质的研究,给出了求解指派问题的两种新算法.新算法能保证把纯伪零点化为零后的新系数矩阵中独立零元素的个数一定增加1.并通过具体算例把两种新算法与匈牙利算法比较,求解过程反映出新算法求解快捷,且能迅速判断指派问题有两组最优解情形.     

用初始条件直接求解常系数线性差分方程

利用线性常系数差分方程描述离散时间系统是信号分析与处理领域中的常用方法和重要手段,激励在n=0时刻开始加入的差分方程求解过程中自由响应系数的确定,通常需要将所给的初始条件经过迭代得到一组n≥0的边界条件,然后将此边界条件代入方程求系数.本文提出了一种直接利用初始条件求解常系数线性差分方程的方法,并对二阶、N阶和有重根情况下给出了较完整的证明,此避免了烦琐的迭代运算,对于从事信号分析与处理具有一定的理论价值和应用价值。     

一种新的求解整型参数估计的预处理方法

本文提出一种新的有效的列选主元QR预处理算法,对线性模型下的整型参数估计问题进行预处理.该预处理算法基于列选主元QR分解,采用迭代过程来获得预处理整型矩阵.由该预处理法得到的上三角矩阵因子R能有效地降低求解整型参数估计问题的时间复杂度,尤其是对高维问题.     

求解旅行商问题的人工蜂群算法

采用人工蜂群算法对旅行商问题进行求解,给出了人工蜂群算法求解该问题的具体方案,对不同的旅行商问题算例进行了仿真实验。结果表明,算法可以有效、快速地找到较小规模问题的最优解。     

奇异方差矩阵的Markowitz''''s证券组合投资决策模型的最优化解法

基于Markowitz证券组合投资模型：min1/2W^tVW，s．t．W^te=1，W^tE（X）=μ0，分析方差矩阵V为一般对称矩阵时的情形，本文推广了证券组合投资模型的一个定理，并分类讨论了一般对称方差矩阵对应的证券组合投资模型的最优解，同时给出了求解最优证券组合的方法。     

Haar小波求解Fredholm-Volterra方程

本文运用Haar小波求解Fredholm-Volterra方程,建立了Haar小波的算子矩阵,利用Haar小波方法求解积分方程的基本思想是将求解积分方程的问题转化为求解一组代数方程组的问题。由于积分方程多出现在物理、工程等诸多应用性研究领域,且解析解难以求出,因此研究其数值解具有重要意义。     

A Unifying Framework and Comparison of Algorithms for Non-negative Matrix Factorisation

Non-negative matrix factorisation (NMF) is an increasingly popular unsupervised learning method. However, parameter estimation in the NMF model is a difficult high-dimensional optimisation problem. We consider algorithms of the alternating least squares type. Solutions to the least squares problem fall in two categories. The first category is iterative algorithms, which include algorithms such as the majorise–minimise (MM) algorithm, coordinate descent, gradient descent and the Févotte-Cemgil expectation–maximisation (FC-EM) algorithm. We introduce a new family of iterative updates based on a generalisation of the FC-EM algorithm. The coordinate descent, gradient descent and FC-EM algorithms are special cases of this new EM family of iterative procedures. Curiously, we show that the MM algorithm is never a member of our general EM algorithm. The second category is based on cone projection. We describe and prove a cone projection algorithm tailored to the non-negative least square problem. We compare the algorithms on a test case and on the problem of identifying mutational signatures in human cancer. We generally find that cone projection is an attractive choice. Furthermore, in the cancer application, we find that a mix-and-match strategy performs better than running each algorithm in isolation.     

基于IK-MD-SA聚类算法的电力数据审计疑点研究

为解决电力行业海量非结构化数据导致审计疑点数据效率、准确性低的难题,本文提出了一种基于迭代IK-MD-SA聚类电力大数据审计疑点算法。首先运用相异性度量算法通过构造相异性矩阵和计算均值相异性改进K-means聚类算法选择初始聚类中心,并将簇均值替换为簇中位数完成后续聚类中心迭代,以消离群点影响聚类结果的准确性。然后利用改进的蜂群算法对聚类结果进行优化,使其保证高运行效率的前提下聚类结果仍具有较高准确性。最后,通过离散性电力数据进行识别潜在疑点试验,验证了所提算法的可行性和有效性。     

Test procedures and test problems for least squares algorithms

Numerous test problems have been introduced in the past twenty years for the purpose of studying and comparing least squares algorithms and computer programs. This paper discusses and classifies some of the useful test problems which have appeared in the literature. A recent large scale test procedure is briefly summarized. Several neat, mathematical examples are displayed. One of these, first introduced by Läuchli, is modified so that it can be solved by the method of inverting a matrix of correlation coefficients. Comparative results from running two types of problems on several different algorithms are given which illustrate some of the factors affecting computational accuracy: choice of algorithm, scaling of the data, tolerance parameters, and iterative refinement.     

On maximum likelihood estimation of stochastic frontier production models

The iterative algorithm suggested by Greene (1982) for the estimation of stochastic frontier production models does not necessarily solve the likelihood equations. Corrected iterative algorithms which generalize Fair's method (1977) and solve the likelihood equations are derived. These algorithms are compared with the Newton method in an empirical case. The Newton method is more time saving than these algorithms.     

Determining the optimal scheme of zoned effluent charges for the control of air pollution

A minimum costly zoned effluent charge program for the control of air pollution is considered paying attention to the general situation where polluters' cost functions of treating pollutant are unknown to the policy authority, and an iterative procedure by which the authority can attain a set of optimal charges is presented. The algorithm consists of steps of estimating the unknown treatment cost functions by observing polluter behavior and steps of revising charges based on the estimated cost functions. In the latter steps, a newly developed solution procedure for the zoned charge programming problem is involved. Simulated use of the algorithm indicates that the iterative charge revision procedure proposed in this paper can effectively provide the optimal scheme of zoned effluent charges.     

有竞争的物流配送中心选址模型研究

文章结合迭代算法、AHP和目标规划方法,在已有的关于有竞争的物流配送中心选址问题的研究成果上进行改进,进行了简单的研究。首先根据配送中心与顾客距离计算新配送中心的最大市场占有率,通过迭代算法获得一些相对较优备选地址,然后通过调查得出候选地址的相关信息,通过层次分析法评估各个备选地址的综合水平,最后通过多目标规划来寻找最好的位置建立物流配送中心,文章主要运用MATLAB,yaahp进行求解。     

基于双自适应Lasso惩罚的随机效应分位回归模型研究

研究目标：解决随机效应分位回归模型中固定效应和随机效应系数同时估计和选择问题。研究方法：对固定效应和随机效应系数同时实施自适应Lasso惩罚,并为参数估计设计交替迭代算法。研究发现：新方法不仅对随机误差分布具有较强的稳健性,而且在不同稀疏度模型下均有着良好的表现,尤其是在高维情形时。研究创新：本文提出的方法在对模型中重要自变量进行选择的同时能够充分考虑随机效应的影响;交替迭代算法不仅有效解决了需要选择两个惩罚参数的困境,而且收敛速度快。研究价值：为实际工作者对面板数据和纵向数据的分析提供了有效的建模方法。     

Fitting nonlinear time-series models with applications to stochastic variance models

New strategies for the implementation of maximum likelihood estimation of nonlinear time series models are suggested. They make use of recent work on the EM algorithm and iterative simulation techniques. The estimation procedures are applied to the problem of fitting stochastic variance models to exchange rate data.     

A NON-SIGN-PRESERVING RAS VARIANT

We have developed a variant of the RAS generalised iterative scaling method that is able to change the sign between successive iterates, and thus fulfil constraints that are infeasible for existing RAS variants. Like earlier RAS variants, our method can handle constraints on arbitrarily sized and shaped subsets of matrix elements, include reliability of the initial estimate and the external constraints, and deal with negative values.     

一种二值图像连通区域标记的简单快速算法

针对传统二值图像连通区域标记需要对图像进行两次扫描的缺点,提出了一钟新的二值图像连通区域标记算法。算法借助创建一与图像等大的标记矩阵,通过深度优先搜索算法对图像进行一次扫描后,将标记编号记录在标记矩阵中。此算法不受连通区域的形状和面积影响,表现出了良好的鲁棒性。最后通过OpenCV对该算法进行了实现并与传统标记算法进行了时间性能比较。