改进的PROMETHEE方法在招标中的应用研究

针对 PROMETHEE方法的局限性 ,对 PROMETHEE方法进行了改进 ,用效用函数取代了优先函数 ,提出了属性权重的确定方法 .应用改进的 PROMETHEE方法 ,对某装备招标中的 6个方案进行了评价 ,取得了较好的效果     

求解非线性方程重根的平方收敛迭代法

研究了具有重根的非线性方程的迭代方法,对基于动力系统的新牛顿类方法作了修改,改进方法仍保持了牛顿方法的二阶收敛性.数值实验结果验证了方法的有效性.     

基于关键链方法的多项目共享人力资源均衡问题及其遗传算法

通过对多项目管理瓶颈的分析,结合关键链方法,设置了瓶颈缓冲,建立了基于关键链方法的多项目管理,为多项目管理提供了一种新的管理方法.将基于关键链方法的多项目管理方法应用于并行多项目共享人力资源冲突管理,建立了基于遗传算法的多项目共享人力资源均衡模型,为缓解多项目共享人力资源供求矛盾提供了一种具体的量化管理方法,并进行了算例分析,证明了模型的有效性、实用性.     

基于模糊结构元表述的模糊数排序

讨论了如何利用结构元理论来解决模糊数的排序问题.首先,给出了四种经典的模糊数排序方法,并证明了这四种方法都可以利用结构元理记来表述;进而,提出了一种基于结构元理论的排序方法,给出了该方法的性质,并同传统方法进行了比较.     

一阶微分方程数值解的一种误差估计方法

针对于微分方程数值解,介绍了一种新的误差估计方法.方法证实了伪谱方法具有精度高速度快的优点,进而引出了修正的伪谱方法.     

基于FA-DEA聚类的模式分析方法及在我国软件园研究中的应用

模式分析方法日益成为现代经济管理研究的主流方法之一,但是目前关于模式分析的结构化方法的研究还不多见.本文提出了基于FA-DEA聚类的模式研究结构化方法,这个方法区别于以往文献的是采用了混合聚类方法,综合运用关键因素的绝对量信息和效率的相对量信息.基于上述方法,本文确定了我国软件园发展的三种发展模式.并对三个模式的条件、特征以及它们之间的分界与演进做了详细的描述.最后,给出了若干建议.     

传统隐式Runge-Kutta方法的转换方法

多级隐式Runge-Kutta(RK)方法簇中,除Gauss类方法是s级2s阶的辛方法以外,Radau类方法和Lobatto类方法既不是s级2s阶的方法也不是辛方法.基于隐式RK方法是一类转换RK方法这一特征,利用V-变换和Pade对角逼近,提出了构造高阶RK方法的转换定理.依据转换定理,导出了s级2s阶的Radau方法和s级2s阶的Lobatto方法.利用V-变换和待定系数法,导出了辛Radau方法和辛Lobatto方法.在此基础上,发现并证明了辛Radau方法是s级2s阶的方法.     

一类新的求解非线性方程的七阶方法

利用权函数法给出了一类求解非线性方程单根的七阶收敛的方法.每步迭代需要计算三个函数值和一个导数值,因此方法的效率指数为1.627.数值试验给出了该方法与牛顿法及同类方法的比较,显示了该方法的优越性.最后指出Kou等人给出的七阶方法是方法的特例.     

关于Leontief产出方程的二级分裂迭代方法

研究Leontief投入产出模型中计算产出向量的迭代方法,基于Leontief产出方程,在矩阵规模很大,直接计算逆矩阵很困难的条件下,通过引入参数并运用二级分裂迭代思想和松弛技术,提出了Leontief产出方程的二级分裂迭代方法,给出了该方法的收敛理论.利用给出的收敛因子的计算方法,讨论了参数的优化选择,数值实例验证了此方法的有效性,表明优化参数能有效提高迭代方法的收敛效率.     

关于特征值的平方和的注记

探讨了特征值的平方和这一计算问题,指出了常用方法的不足之处,并在深入研究方阵相似的基础之上弥补了这一不足,彻底解决了这一问题,此外运用这种方法还能解决特征值高次幂之和与多项式之和的计算问题.最后文中给出了一种新的计算特征值平方和的方法,这种方法能够回避第一种方法的不足,但缺点是不易推广.     

基于概念的数学系统及其结构

随着科学技术的发展，应用定量分析的数学方法已从自然科学发展到社会科学、思堆科学．为了处理这些问题的需要，许多学者建立了多种数学模型和数学方法，这些模型和方法都直接或间接地涉及到概念，因此归纳并研究基于概念的数学方法显得很有必要。本文应用系统的方法，尝试络出数学系境的概念，并建立了基于概念的数学系统及其结构的一般方法，期望更多的学者予以关注和研究。     

ASYMPTOTICALLY OPTIMAL SUCCESSIVE OVERRELAXATION METHODS FOR SYSTEMS OF LINEAR EQUATIONS

We present a class of asymptotically optimal successive overrelaxation methods for solving the large sparse system of linear equations. Numerical computations show that these new methods are more efficient and robust than the classical successive overrelaxation method.     

Markov Chain Monte Carlo With Mixtures of Mutually Singular Distributions

Markov chain Monte Carlo (MCMC) methods for Bayesian computation are mostly used when the dominating measure is the Lebesgue measure, the counting measure, or a product of these. Many Bayesian problems give rise to distributions that are not dominated by the Lebesgue measure or the counting measure alone. In this article we introduce a simple framework for using MCMC algorithms in Bayesian computation with mixtures of mutually singular distributions. The idea is to find a common dominating measure that allows the use of traditional Metropolis-Hastings algorithms. In particular, using our formulation, the Gibbs sampler can be used whenever the full conditionals are available. We compare our formulation with the reversible jump approach and show that the two are closely related. We give results for three examples, involving testing a normal mean, variable selection in regression, and hypothesis testing for differential gene expression under multiple conditions. This allows us to compare the three methods considered: Metropolis-Hastings with mutually singular distributions, Gibbs sampler with mutually singular distributions, and reversible jump. In our examples, we found the Gibbs sampler to be more precise and to need considerably less computer time than the other methods. In addition, the full conditionals used in the Gibbs sampler can be used to further improve the estimates of the model posterior probabilities via Rao-Blackwellization, at no extra cost.     

Persistence of nonhyperbolic measures for <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript>-diffeomorphisms

In the space of diffeomorphisms of an arbitrary closed manifold of dimension ≥ 3, we construct an open set such that each difteomorphism in this set has an invariant ergodic measure with respect to which one of its Lyapunov exponents is zero. These difteomorphisins are constructed to have a partially hyperbolic invariant set on which the dynamics is conjugate to a soft skew product with the circle as the fiber. It is the central Lyapunov exponent that proves to be zero in this case, and the construction is based on an analysis of properties of the corresponding skew products.     

Stochastic partitions of sub-σ-fields of a probability measure space

Lattice and measure theoretic methods are used to characterize the system of implications of a set of stochastic partitions of collections of sub-σ-fields of a probability measure space.     

A Decision Criterion for the Optimal Number of Clusters in Hierarchical Clustering

Clustering has been widely used to partition data into groups so that the degree of association is high among members of the same group and low among members of different groups. Though many effective and efficient clustering algorithms have been developed and deployed, most of them still suffer from the lack of automatic or online decision for optimal number of clusters. In this paper, we define clustering gain as a measure for clustering optimality, which is based on the squared error sum as a clustering algorithm proceeds. When the measure is applied to a hierarchical clustering algorithm, an optimal number of clusters can be found. Our clustering measure shows good performance producing intuitively reasonable clustering configurations in Euclidean space according to the evidence from experimental results. Furthermore, the measure can be utilized to estimate the desired number of clusters for partitional clustering methods as well. Therefore, the clustering gain measure provides a promising technique for achieving a higher level of quality for a wide range of clustering methods.     

测度链上具有变号非线性项微分方程的正解(英文)

本文研究了测度链上具有变号非线性项微分方程的问题.利用拓扑方法,获得了此微分方程的正解存在性结果,推广和改进了一些文献中相应的结果.     

ON THE CONVERGENCE DOMAIN OF THEMATRIX MULTISPLITTING RELAXATION METHODS FOR LINEAR SYSTEMS

The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473-486) is further investigated.The investigations show that these relaxation methods really have considerably larger convergence domains.     

A CLASS OF ASYNCHRONOUS MATRIX MULTI-SPLITTING MULTI-PARAMETER RELAXATION ITERATIONS

1.IntroductionMultisplittingmethodsforgettingthesolutionoflargesparsesystemoflinearequationsAx=b,A=(and)6L(Rn)nonsingular,x=(x.),b=(b.)eR"(1.1)areefficientparalleliterativemethodswhicharebasedonseveralsplittingsofthecoefficientmatrixAEL(R").Following[11th…     

On relaxed greedy randomized Kaczmarz methods for solving large sparse linear systems

For solving large sparse systems of linear equations by iteration methods, we further generalize the greedy randomized Kaczmarz method by introducing a relaxation parameter in the involved probability criterion, obtaining a class of relaxed greedy randomized Kaczmarz methods. We prove the convergence of these methods when the linear system is consistent, and show that these methods can be more efficient than the greedy randomized Kaczmarz method if the relaxation parameter is chosen appropriately.