Matlab程序的代码移植性研究

本文分析了Matlab代码移植的三种方案；基于ActiveX技术的移植方案。基于DDE数据动态交换技术的代码移植方案和基于DLLs技术的代码移植方案。指出了代码移植时的注意事项，并对三种方案作了比较。     

论极限教学的解决方案

首先探讨了极限ε语言的思维复杂性,接着介绍了种种极限教学方案以及笔者自身的实践,在回顾微积分的历史和比较各种方案后,根据教育学原理提出了一种新的极限教学的组合方案.     

定期连续调查的一种优选抽样方案

蔡择林．定期连续调查的一种优选抽样方案．数理统计与管理，１９９８，１７（２），２６～２９．在数据可回溯的定期连续调查中，考虑到老单位被保留下来时，调查费用一般较低这一因素，本文在确定的最优准则下，给出了一种最优抽样方案，并将该方案与一些常用的方案作了比较。     

基于云化双重AHP模型的地铁施工方案选择研究

根据专家对于方案评判指标重要性的自然思维对比过程和形成数据的特点,提出了云化双重AHP模型对备选方案进行选优,并应用于地铁施工方案选择.专家的自然思维对比过程分两次进行.第一次是赖于工程背景,不同施工方案之间相同评判指标的比较;第二次是不考虑实际工程背景下的各指标比较.使用云模型嵌入AHP是为了对专家提供的不确定信息进行处理.基于上述两点考虑构建了云化双重AHP模型.分析了4种隧道施工方案,得到了方案选优指标.分析结果表明:对于给定的工程背景,使用盾构法施工是最优的.最后将该模型与现有4种模型进行对比,说明了模型的相对优点.     

二阶抽样中二级单位总样本量的分配

本文讨论了二阶抽样中一阶抽样为不等概率抽样、二阶抽样为简单随机抽样时,二级单位总样本量的几种分配方案。给出各种分配方案下总体总值的Horvitz-Thompson估计量的方差。并加以比较,最后给出最优分配方案。     

具有多种信息形式的随机多属性决策方法研究

针对属性值为随机变量、清晰数和模糊数三种信息形式的多属性决策问题,提出了一种决策分析方法.在本文中,首先给出了混合占优准则的描述及相关分析,并提出了混合占优度的定义及其计算公式;然后,依据混合占优准则判断并确定两两方案之间比较的占优关系,进而计算得到两两方案之间比较的混合占优度,并构建相应的混合占优度矩阵,在此基础上,运用PROMETHEE Ⅱ方法得到方案的排序结果.最后,通过一个算例说明了本文给出方法的可行性和有效性.     

基于Lagrange插值多项式的接近性关联度决策模型及其应用

针对实数情形的灰色关联决策问题,提出了一种选择最优方案的新方法:首先计算出各个方案和理想方案的Lagrange插值多项式,并利用黎曼积分计算出各个方案和理想方案两曲线之间的面积,进而构造接近性关联度,通过比较接近性关联度来选择最优方案.然后针对区间灰数情形,提出分别计算出各方案的下界序列到理想方案的下界序列的接近性关联度,各方案的上界序列到理想方案的上界序列的接近性关联度后再计算两者的新型综合关联度,并通过比较综合关联度来选择最优方案.最后通过实数和区间灰数两个不同的算例来进一步验证了该方法的可行性、合理性和有效性.     

基于模糊语言判断矩阵和FIOWA算子的有限方案决策法

定义一种模糊的导出有序加权平均(FIOWA)算子，给出方案之间比较的模糊语言标度。运用模糊语言标度构造出模糊语言判断矩阵，并提出一种基于模糊语言判断矩阵和FIOWA算子的有限方案决策方法。该法利用FIOWA算子对模糊语言信息进行集结，并利用已有的三角模糊数排序公式求得决策方案的排序。     

层次分析法在身份鉴别方案选择中的应用

针对身份鉴别方案比较的问题,采用层次分析法AHP(Analytic HierarchyProcess)建立了身份鉴别方案比较的数学模型,定量分析了指纹识别、人脸识别、语音识别、虹膜识别、静脉红外识别和DNA识别六种生物识别技术在身份鉴别中的综合表现,并做出评价.评价结果对重要场合安全检查中人员身份鉴别方法的选择有一定的指导意义.     

政府规制下RSC的激励研究

本文用委托-代理理论讨论了政府规制下逆向供应链的激励问题,在补贴、惩罚为独选择的激励方案有三种:(1)奖励、惩罚同步实施的方案;(2)仅实施惩罚的方案;(3)仅实施奖励的方案,通过对三种不同方案的分析比较,得出:奖励、惩罚同步实施的方案是政府最优的激励方案.同时文章还分析了信息不对称所带来的代理成本问题.所得结论,对政府环境部门在制定环境补贴政策和决策环境监督水平具有重要的理论和现实意义,为进一步研究更加复杂的政府和企业的合约与监督机制奠定了理论基础.     

几类改进的新的两步六阶Chebyshev-Halley方法

利用权函数法,给出非线性方程求根的Chebyshev-Halley方法的几类改进方法,证明方法六阶收敛到单根.Chebyshev-Halley方法的效率指数为1.442,改进后的两步方法的效率指数为1.565.最后给出数值试验,且与牛顿法,Chebyshev-Halley 方法及其它已知的方程求根方法做了比较.结果表明方法具有一定的优越性.     

Interior-point methods for linear programming: a review

The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with infeasible interior methods and homogeneous self-dual methods for linear programming. Also discussed are some theoretical issues in interior-point methods like dependence of complexity bounds on some non-traditional measures different from the input length L of the problem. Finally, the paper concludes with remarks on the comparison of interior-point methods with the simplex method based on their performance on NITLIB suite, a standard collection of test problems.     

Waveform Relaxation Methods for Lie-Group Equations

In this paper, we derive and analyse waveform relaxation (WR) methods for solving differential equations evolving on a Lie-group. We present both continuous-time and discrete-time WR methods and study their convergence properties. In the discrete-time case, the novel methods are constructed by combining WR methods with Runge-Kutta-Munthe-Kaas (RK-MK) methods. The obtained methods have both advantages of WR methods and RK-MK methods, which simplify the computation by decoupling strategy and preserve the numerical solution of Lie-group equations on a manifold. Three numerical experiments are given to illustrate the feasibility of the new WR methods.     

The global Hessenberg and CMRH methods for linear systems with multiple right-hand sides

In this paper, we introduce two new methods for solving large sparse nonsymmetric linear systems with several right-hand sides. These methods are the global Hessenberg and global CMRH methods. Using the global Hessenberg process, these methods are less expensive than the global FOM and global GMRES methods [9]. Theoretical results about the new methods are given, and experimental results that show good performances of these new methods are presented.     

Preservation of equilibria for symplectic methods applied to Hamiltonian systems

In this paper, the linear stability of symplectic methods for Hamiltonian systems is studied. In par- ticular, three classes of symplectic methods are considered： symplectic Runge-Kutta （SRK） methods, symplectic partitioned Runge-Kutta （SPRK） methods and the composition methods based on SRK or SPRK methods. It is shown that the SRK methods and their compositions preserve the ellipticity of equilibrium points uncondi- tionally, whereas the SPRK methods and their compositions have some restrictions on the time-step.     

Fourth-Order Splitting Methods for Time-Dependant Differential Equations

This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.     

QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS

1. IntroductionInvestigating whether a numerical method inherits some dynamical properties possessed bythe differential equation systems being integrated is an important field of numerical analysisand has received much attention in recent years See the review articlesof Sanz-Serna[9] and Section 11.16 of Hairer et. al.[2] for more detail concerning the symplectic methods. Most of the work on canonical iotegrators has dealt with one-step formulaesuch as Runge-Kutta methods and Runge'methods …     

Mehar’s methods for fuzzy assignment problems with restrictions

In this paper, limitations of existing methods [5, 11] for solving fuzzy assignment problems (FAPs) are pointed out. In order to overcome the limitations of existing methods, two new methods named Mehar’s methods are proposed. To show the advantages of Mehar’s methods over existing methods, some FAPs are solved. The Mehar’s methods can solve the problems solved by existing methods as well as those which cannot be solved by existing methods.     

New Multivalue Methods for Differential Algebraic Equations

Multivalue methods are slightly different from the general linear methods John Butcher proposed over 30 years ago. Multivalue methods capable of solving differential algebraic equations have not been developed. In this paper, we have constructed three new multivalue methods for solving DAEs of index 1, 2 or 3, which include multistep methods and multistage methods as special cases. The concept of stiff accuracy will be introduced and convergence results will be given based on the stage order of the methods. These new methods have the diagonal implicit property and thus are cheap to implement and will have order 2 or more for both the differential and algebraic components. We have implemented these methods with fixed step size and they are shown to be very successful on a variety of problems. Some numerical experiments with these methods are presented.     

Applications of doubly companion matrices

Doubly companion matrices are used as a tool to analyze the ESIRK and DESIRE methods, and the general linear methods satisfying the IRKS property. These methods can be considered as extensions of the DIRK and SIRK Runge–Kutta methods, and were introduced to overcome some of the undesirable properties of these methods. A connection between the ESIRK and DESIRE methods, and IRKS methods is also established. Several low order methods are given.