关键词： 数学选择题   估算法   求解   《考试说明》   能力要求   近似计算   估计   算式  

摘要： 所谓估算,是指在计算测量中无法或没有必要进行精确判断时,根据具体条件及有关知识,对事物的数量或算式的结果迅速作出大概的估计所采取的计算方法.历年《考试说明》对数学能力要求中都有＂能根据要求对数据进行估计,并能近似计算＂的要求.

关键词： Dense linear algebra   Power consumption   Multi-core processors   DVFS  

摘要： This paper addresses the efficient exploitation of task-level parallelism, present in many dense linear algebra operations, from the point of view of both computational performance and energy consumption. The strategies considered here, referred to as the Slack Reduction Algorithm (SRA) and the Race-to-Idle Algorithm (RIA), adjust the operation frequency of the cores during the execution of a collection of tasks (in which many dense linear algebra algorithms can be decomposed) with very different approaches to save energy. The procedures are evaluated using an energy-aware simulator, which is in charge of scheduling/mapping the execution of these tasks to the cores, leveraging dynamic frequency voltage scaling featured by current technology. Experiments with this tool and the practical integration of the RIA strategy into a runtime show the energy gains for two versions of the QR factorization.

关键词： Heat exchangers   Optimization   Boilers   Heat   Heat transfer coefficients   Modeling   Flow (Dynamics)   Boiling   Design   Sensitivity analysis   Organic Rankine cycle   Genetic algorithms   Pressure drop   Pareto optimization  

摘要： In the present paper a mathematical model for a mini-channel heat exchanger is proposed. Multiobjective optimization using genetic algorithm is performed in the next step in order to obtain a set of geometrical design parameters, leading to minimum pressure drops and maximum overall heat transfer coefficient. Multiobjective optimization procedure provides a set of optimal solutions, called Pareto front, each of which is a trade-off between the objective functions and can be freely selected by the user according to the specifications of the project. A sensitivity analysis is also carried out to study the effects of different geometrical parameters on the considered functions. The whole system has been modeled based on advanced experimental correlations in MATLAB environment using a modular approach.

关键词： Nonlinear equations   Genetic algorithm   Augmented Lagrangian function   Optimization   Initial interval  

摘要： Solving of nonlinear algebraic equations is a prominent problem in science and engineering. In this study, the systems of these equations were solved using genetic algorithms. Three distinctive groups of the equations were studied: a single nonlinear equation, a simple set of nonlinear equations and a complex set of nonlinear equations. In the two first cases, the problem was converted into the unconstrained optimization problem with some simple mathematical relations. Then, the genetic algorithm was used to solve the problem. In the complex nonlinear equations, the problem was changed into the constrained optimization problem and genetic algorithm, in conjunction with augmented Lagrangian function has been used to find the solution. The proposed scheme has been evaluated with five benchmarks with different applications. Moreover, the sensitivity analysis of the method to initial interval and size of population has been studied. The results have a high precision and show good agreement in comparison with conventional methods. (C) 2013 Elsevier Inc. All rights reserved.

关键词： 数学算法   计算机编程   优化   研究  

摘要： 数学算法是数学学科中的一种精华内容,算法是一种能够将诸多问题进行归类总结,从而实现统一计算的一种数学思想。计算机技术的最基础的应用就是数学算法,其编程语言以及编程逻辑就是建立在数学的基础上。因此,研究计算机编程一定要从其算法的基础进行研究。不仅如此,数学算法对于计算机编程的优化还有非常广泛的应用。因此,本文将通过对数学算法的研究,进而解决其在计算机编程中的优化作用。

关键词： 粒子群算法   学习因子   惯性权重   统一性   基准函数  

摘要： 粒子群算法(PSO)中惯性权重和学习因子的独自调整策略削弱了算法进化过程的统一性和粒子群的智能特性,很难适应复杂的非线性优化,为此提出一种利用惯性权重来控制学习因子的PSO算法。该算法将学习因子视作惯性权重的线性、非线性以及三角函数,在惯性权重随时间线性或非线性递减的过程中,学习因子发生相应的递减或递增变化,进而通过增强两者之间的相互作用来平衡算法的全局探索和局部开发能力,更好地引导粒子进行优化搜索。同时为了分析惯性权重和学习因子的融合性能,采用线性和非线性权重法进行比较,测试函数的优化结果表明了采用非线性递减权重的优越性。最后通过对多个基准测试函数的优化分析,并与带有异步线性变化和三角函数学习因子调整方法的PSO进行比较发现,该策略利用惯性权重调整学习因子,能达到平衡粒子个体学习能力和向群体学习能力的作用,提高了算法的优化精度。

关键词： 多特征提取   函数   识别   特征值  

摘要： 数据建模优化在多特征提取领域应用广泛,基于统计特征和基于结构特征的识别算法需要在数学建模优化下实施,可以改变图像的输入结构,从而能够对图形的统计特征进行提取,采取网格划分方法,对图像进行划分,然后对网格内文字像素进行比对,保证文字图像能够通过细分类模式进行识别.