一个修正的PVT算法

对Fkshima(1998）所提出的PVT算法给出一种修正算法，称为修正PVT算法，这一修正算法对PVT原算法中的并行步中的停止准则和同步步骤作了修正。修正PVT算法的停止条件对PVT原算法的停止条件弱，因此更适用于并行计算，并且计算时间比PVT原算法少。     

模拟退火算法的改进及其应用

模拟退火算法是随机优化近似算法。本文首先介绍其物理背景和一般形式，然后通过对算法增加记忆和返回两个功能以及在算法之后链接一个局部搜索过程，改善了算法性能，接着将改进算法应用于解旅游商问题，最后对该算法作简要的性能评论。     

两台机器超载实时系统的On-line算法

对超载实时系统的On—line算法中的SR算法作了修改，提出了NSR算法，并证明NSR算法的竞争比至少为2／5，因而它比SR算法更为优异．     

算法教学中丰富的数学思想

掌握算法和算法思想是信息时代对学生提出的一项新要求，算法进入中学数学课程也是世界课程改革的一大潮流．我国高中数学新课程就顺应了这种趋势，第一次把算法引入高中数学课程．新课标中提出：“学生要通过对具体问题过程与步骤的分析，体会算法思想，了解算法的含义．”在教学说明意见部分提出，要将算法思想渗透到高中课程的其他相关内容．从广义上讲，每一个问题（特别是数学问题）的解决都对应着一个算法，研究问题的方法就是研究算法．而算法思想，应该包括两个层面：     

环Z／（m）上两种序列综合算法之间的关系

有限域Fq上单条序列的综合算法有著名的Berlkamp-Massey算法(简记B-M算法)，Reeds和Sipane(1985)将这一算法推广到整数同余类环Z／(m)上．作者曾利用推广的Gr6bner基理论，蛤出了环Z／(m)上单条及多条序列的新的综合算法，简称G-算法．本文讨论这两种序列综合算法之间的关系，并证明了G-算法和B-M算法对域上序列的综合是等价的；对环Z／(m)上的序列，通过对G-算法适当改进，可以顺序得到由推广的B-M算法求得的特征多项式．     

一类教育最优投资模型的快速瓶颈消除算法

本提出了一类教育最优投资模型的快速瓶颈消除算法，给出了算法的思想和具体迭代过程，对算法的最优性进行了证明。最后通过实例给出了算法直观的表上作业法。该算法迭代次数非常少，是一种实用的好算法。     

有界变量线性规划的基线算法

本文对有界变量线性规划的算法进行了研究，得到了一种解此问题的新算法。文中根据基线算法的算法原理，通过对BL表的旋转，在各变量满足界约束的条件下，使目标函数值不断增大，直至得到有界硬上界，从而得到问题的最优解。文中给出了有界变量线性规划基线算法的计算步骤，并给出了一个例子。与单纯形法相比，采用基线算法解有界变量线性规划操作更简单。迭代次数少，解题速度更快。     

基于链接学习的生物地理学算法求解置换流水车间调度问题

针对置换流水车间调度问题的特性，提出了一种基于链接学习的生物地理学算法(Biogeography-based optimization based on linkage learning, LLBBO)来对其求解。算法以生物地理学算法为架构，使用反向学习方法(Opposition-based learning, OBL)生成初始解，依据群体适应度值将群体分为优秀群体和劣势群体，使用信息熵的概念以及数理统计方法通过对这两个群体进行统计，分别建立概率矩阵模型以构建一种链接学习模型称为链接区块，使用链接区块依照算法迁移率对群体进行迁移操作实现群体更新。为进一步改善算法的搜寻性，提出一种NEH序列重组法对解序列执行局部搜索以进一步提高适应度。最后运用所提的LLBBO算法通过对基准例题的仿真测试和算法比较验证了所提算法的有效性。     

基于Stacking算法集成的我国信用债违约预测

通过对2014～2019年我国信用债违约案例的原因分析及相关文献综述，从债券资质、债务主体、财务数据、宏观因素四个维度构建债券违约的指标体系，利用随机森林算法优化，研究发现当影响因素选择18项与37项时，样本内外预测结果达到均衡。基于不同角度的七种算法对比分析，择优选取三种作为底层算法：随机森林算法、梯度提升决策树算法与贝叶斯算法，并结合逻辑回归算法为次级训练算法融合构建基于Stacking算法集成的债券违约预测模型。实证结果表明，第一，Stacking算法的双重集成作用相对底层的单次集成总体精确度提升了1%到8%;第二，对不同指标数量的Stacking算法集成模型的评估表明所构建的指标体系提高了预测水平；第三，基于样本内外预测均衡的底层算法选择方法有效可取，分别纳入相对劣势的底层算法时，会逐渐影响模型稳定性。研究成果可以为我国债券市场风险管理提供技术支持与参考。     

一类非单调线性互补问题的高阶Dikin型仿射尺度算法

对于一类非单调线性互补问题提出了一个新算法：高阶Dikin型仿射尺度算法，算法的每步迭代．基于线性规划Dikin原始-对偶算法思想来求解一个线性方程组得到迭代方向，再适当选取步长，得到了算法的多项式复杂性。     

A computational comparison of some branch and bound methods for indefinite quadratic programs

The aim of this paper is to discuss different branch and bound methods for solving indefinite quadratic programs. In these methods the quadratic objective function is decomposed in a d.c. form and the relaxations are obtained by linearizing the concave part of the decomposition. In this light, various decomposition schemes have been considered and studied. The various branch and bound solution methods have been implemented and compared by means of a deep computational test.      

THE APPROXIMATE COMPUTATION OF HYPERSINGULAR INTEGRALS ON INTERVAL

In this paper some numerical methods for computing hypersingular integrals on interval are given. Using geometric meshes, these methods lead 10 an exponential convergence in the range of engineering compulation. A numerical example shows their effeclivity and accuracy.     

求解大型线性方程组的一类非定常内外迭代法

1 引 言 求解大型线性方程组 Ax=b, A∈R~(?),det(A)≠0. x,b∈R~n (1.1)的内外迭代法,首先由Nichols于1973年提出。由于这类算法在求解大型问题。特别对由边值问题离散化得到的大型稀疏方程组求解,显示了优越性,而受到众多的关注。1991年,Lanzkron.Rose.Szvld等人进一步降其发展成为成套迭代法,为预条件组的近似及同步和     

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois.     

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.     

Symplectic Runge-Kutta methods of high order based on W-transformation

In this paper , characterizations of symmetric and symplectic Runge-Kutta methods based on the W-transformation of Hairer and Wanner are presented. Using these characterizations, we construct two families symplectic (symmetric and algebraically stable or algebraically stable) Runge-Kutta methods of high order. Methods constructed in this way and presented in this paper include and extend the known classes of high order implicit Runge-Kutta methods.     

Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations

The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. They are now mostly used as precondition-ers for the popular iterative solvers. In this paper a generalization of these methods are proposed and their convergence properties are studied. Some numerical experiments are given to show the efficiency of the new methods.     

On Covering Methods for D.C. Optimization

Covering methods constitute a broad class of algorithms for solving multivariate Global Optimization problems. In this note we show that, when the objective f is d.c. and a d.c. decomposition for f is known, the computational burden usually suffered by multivariate covering methods is significantly reduced. With this we extend to the (non-differentiable) d.c. case the covering method of Breiman and Cutler, showing that it is a particular case of the standard outer approximation approach. Our computational experience shows that this generalization yields not only more flexibility but also faster convergence than the covering method of Breiman-Cutler.     

两类求解刚性常微分方程的指数拟合法

本文提出了两类不需计算高阶全导数的３价和４价指数拟合的单步法，这些方法分别改进或推广了［１］－［４］中的某些方法，初步数值试验表明，这些方法用于求解某些ｓｔｉｆｆ问题，优于［１］－［４］中同阶方法。     

A class of globally convergent conjugate gradient methods

Conjugate gradient methods are very important ones for solving nonlinear optimization problems, especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods were usually analyzed individually. In this paper, we propose a class of conjugate gradient methods, which can be regarded as some kind of convex combination of the Fletcher-Reeves method and the method proposed by Dai et al. To analyze this class of methods, we introduce some unified tools that concern a general method with the scalar βk having the form of φk/φk-1. Consequently, the class of conjugate gradient methods can uniformly be analyzed.