关键词： C语言   计算机辅助计算   程序设计   CT   S100599   C语言   CT   S036572   计算机辅助计算   CT   S008424   程序设计  

摘要： 本书主要研究利用C++语言编写各种与实数和复数有关的数学算法，如线性代数、矩阵运算、实数方程求解、插值、拟合、数值积分、微分方程等等。书中所有程序均调试通过。本书提供的类库为作者独创，具有编程容易、效率高的特点。

关键词： 全局优化   组合优化   旅行商问题   人工神经网络   正交设计方法   模拟退火   遗传算法  

摘要： 该文上篇将外部罚函数的思想融入到Hopfield网络当中,得到了一种新的时变反馈神经网络模型.作者将增长罚因子引入到时常反馈神经网络模型当中,使其求解旅行商问题的成功率和收敛速度都显著提高,网络参数的敏感性也得到了一定的改善,并通过大量的数字模拟试验使新模型得到了实践上的支持.最后,我们运用正交设计方法,对网络参数、罚因子参数及模型结构进行了优化选择,使得TSP问题解的质量得到了进一步提高.下篇中,作者给出了一种新的遗传算法早熟控制策略,包括种群规模和最大进化代数等控制参数的经验公式以及交叉概率和变异概率的自适应调整策略.同时将模式识别理论中模式相关的概念和神经元的响应函数引入到标准遗传算法(SGA)中,定义了两个染色体之间的共享函数,用它进行适应值的共享小生境标定,并进一步做适应值的Boltzman标定,实现了一种新的混合遗传算法.大量的算例表明,这种新算法比SGA有更强的全局寻优能力.

关键词： Matrix algebra  

摘要： The increasing availability of advanced-architecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra - in particular, the solution of linear systems of equations - lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to exploit these advanced-architecture computers. We discuss two broad classes of algorithms: those for dense, and those for sparse matrices. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： convex nonlinear programming   descent method   interior points   gravitational method  

摘要： This paper describes a constrained optimization method that was inspired by the physical equivalent of a small ball that, propelled only by gravity, is dropped from an initial point inside a full-dimensional body, represented by the set of feasible solutions. The ball will eventually hit one of the boundaries of the given set, at which point it will bounce off and continue until it comes to rest at some point. We prove that this point is a local minimum.

关键词： 模糊模型   隶属度函数   模拟退火   学习算法  

摘要： 模糊规则的提取和模糊隶属度函数的学习是模糊系统设计中重要而困难的问题 .文中探讨了Takagi Sugeno模糊模型的隶属度函数学习问题 ,建立了基于模拟退火的模糊隶属度函数学习算法 ,给出了用于验证该算法有效性的仿真实例 .

关键词： algebraic path problem   uniform recurrence equations   dependence graph   systolic architectures  

摘要： In this paper, we are interested in solving the algebraic path problem (APP) on regular arrays. We first unify previous contributions with recurrence transformations. Then, we propose a new localization technique without long-range communication which leads to a piecewise affine scheduling of 4n + Theta(1) steps, where n is the size of the problem. The derivation of a locally connected space-time minimal solution with respect to the new scheduling constitutes the second contribution of the payer. This new design requires n(2)/3 + Theta(n) elementary processors and solves the problem in 4n + Theta(1) steps, and this includes loading and unloading time. This is an improvement over the best previously known bounds. 0 2000 Elsevier Science B.V. All rights reserved.

关键词： 中小学   数学教学   数的概念   运算法则  

关键词： geometric algorithm   complexity   point-in-polygon test  

摘要： Linking number is a basic invariant of a closed curve in topology. In this paper, linking number is generalized in a computational way to reflect the spatial relationship between a point and a line segment, an are, a plane subdivision, a three-dimensional shape, a three-dimensional object and a three-dimensional space subdivision. An algebraic algorithm for the point-in-polygon test is devised on the base of the generalized linking number. The algorithm is characterized by the algebraic property that the linking number of a point to a polygon is merely the arithmetic sum of the linking numbers of the point to all the line segments of the polygon. The algorithm takes intersection into consideration, but no intersection is actually computed. It calculates the linking number, but no trigonometric function is processed. Detailed time complexity analysis shows that this algorithm greatly improves currently existing algorithms for the point-in-polygon test. Another achievement of this paper is the consistent and successful extension of the algebraic algorithm for the point-in-polygon test to point inclusion queries in two-dimensional objects, plane subdivisions, three-dimensional shapes, three-dimensional objects and three-dimensional space subdivisions. All these algorithms retain the algebraic character. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： integer programming   algebraic geometry   Groebner basis  

摘要： We propose a new algorithm for solving integer programming (IP) problems that is based on ideas from algebraic geometry. The method provides a natural generalization of the Farkas lemma for IP, leads to a way of performing sensitivity analysis, offers a systematic enumeration of all feasible solutions, and gives structural information of the feasible set of a given IP. We provide several examples that offer insights on the algorithm and its properties.

关键词： 煤矿   空车分配   动态规划   计算机算法  

摘要： 运用计算机编制矿区的最优空车分配方案 ,使全矿的总落地煤最少 .建立了数学定义和数学模型 ,给出空车分配问题的一系列最优性准则及化简方法 ,有效地降低了求解该问题的规模 .应用动态规划方法编制了求解该问题最优解的计算机算法 ,分析了该算法的复杂性和有效性 .通过对一个实例的计算和结果的分析 ,说明该算法在实际应用中是可行的 .