关键词： 计算机算法   方程求根   数学理论   数学问题   求解问题   求和问题   求值问题   集合问题  

摘要： 谈及经典数学理论很多读者都应该不会陌生，比如像等式方程（组）的求解问题、数列求和问题、微积分的求值问题、集合问题、概论问题，以及一些经典数学问题如哥尼斯堡七桥问题、海盗分金问题等等，这都是我们学生时代所熟知的。但是，本文所要谈的并不是关于以上这些数学问题是怎么样解决的，那是数学课上的内容。本文所要谈的是像上面的这些经典数学问题是如何用计算机实现的。说到这里可能有些读者要问了：计算机和经典数学有关系吗？这可是两个不同的学科噢!的确，十几年前人们很难把这两个学科联系在一起。但近几年，

关键词： Bernoulli equation   linear and nonlinear matrix equations   matrix sign function   control and systems theory   parallel linear algebra libraries  

摘要： We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory. Here, we discuss algorithms based on a generalization of the Newton iteration for the matrix sign function. The algorithms are easy to parallelize and provide an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.

关键词： mathematical programs with equilibrium constraints   mathematical programs with complementarity constraints   partial MPEC-LICQ   global convergence   piecewise stationary points  

摘要： We propose a merit-function piecewise SQP algorithm for mathematical programs with equilibrium constraints (MPEC) formulated as mathematical programs with complementarity constraints. Under mild conditions, the new algorithm is globally convergent to a piecewise stationary point. Moreover, if the partial MPEC linear independence constraint qualification (LICQ) is satisfied at the accumulation point, then the accumulation point is an S-stationary point.

关键词： 中学数学   算法   教学   课程标准   数学教材   高中数学   信息化  

摘要： 根据课程标准，普高数学教材增加了算法的有关内容．这一举措在促进国民信息化素养不断提高的同时，有利于加深每一位学生对数学的整体认识．但作为高中数学的新增内容，如何教好算法这部分内容需要经过长时间的摸索，在本文中结合教学实际谈一些自己的看法．

关键词： 贝叶斯网络   EM算法   PL-EM算法   MPI  

摘要： 针对大样本条件下EM算法学习贝叶斯网络参数的计算问题,提出一种并行EM算法(Parallel EM,PL-EM)提高大样本条件下复杂贝叶斯网络参数学习的速度.PL-EM算法在E步并行计算隐变量的后验概率和期望充分统计因子;在M步,利用贝叶斯网络的条件独立性和完整数据集下的似然函数可分解性,并行计算各个局部似然函数.实验结果表明PL-EM为解决大样本条件下贝叶斯网络参数学习提供了一种有效的方法.

关键词： 配送中心   分批拣货   订单   模型   算法  

摘要： 以最小化行走距离为目标,构造了拣货作业中订单分批问题的数学模型,在一些模型假设的基础上,给出了订单分批拣货问题的节约启发式算法。并通过算例分析,表明此算法的订单分批结果优于传统的先到先服务分批结果,为实现拣货作业中的订单优化分批提供了一个新方法。

关键词： clones of algebras   Codd's algebra   functional completeness   lattice of maximal subalgebras   n-ary relation   composition of n-relations   functionality of n-relations  

摘要： Clones of algebras of n-relations are examined. These clones include algebras equipotent to Codd's algebra. The results obtained earlier for semigroup (grammatical and algorithmic) clones are extended to clones of algebras of functional n-relations. One-dimensional and multidimensional computing structures and related object domains are outlined.

关键词： adaptive finite elements   rosenbrock algorithm   computational electrochemistry   simulation   error control   dynamic adsorption   surface reactions  

摘要： Adaptive algorithms promise to provide general tools for the solution of dynamic electrochemical simulation models. We describe a modeling strategy which enables an adaptive step size selection. in time based on the control of errors in the concentrations both of dissolved and adsorbed molecules and additionally in the electrochemical response, e.g. the current. Combined with automatic finite element grid adaption in space, a robust algorithm is obtained and included in the EChem++ problem solving environment. Simulations of chronoamperometric and cyclic voltammetric experiments in a one-dimensional cell geometry under linear diffusion conditions demonstrate the applicability of the approach. Provisions to integrate potential jumps in the time step control enable a flexible handling of multi-pulse chronoamperometry. Further applications include fast and slow kinetic adsorption processes and those including surface reactions. (c) 2007 Elsevier B.V. All rights reserved.

关键词： 多层卫星网络   星间链路   数学模型   路由算法  

摘要： 建立了多层卫星网络的层次数学模型,在对数学模型研究的基础上,提出了一种适合多层卫星网络应用的层次路由算法.仿真结果表明,该算法具有较快的计算速度,降低了拓扑更新的通信开销,随着链路利用率的增加具有很好的时延性能,能够有效地提高空间信息网络的路由性能.