Consistent Initialization for Nonlinear Index-2 Differential–Algebraic Equation: Large Sparse Systems in MATLAB

An important component of any initial-value solver for higher-index differential–algebraic equations consists in the computation of consistent initial values. In a recent paper [5], an algorithm is proposed which is applicable to a very general class of index-2 systems. Unfortunately, the computational expense is rather high. We present a modification of this approach, which gives rise to a MATLAB implementation capable of handling systems of moderate dimension (several thousands of unknowns). The algorithm is illustrated by examples.     

用计算机实现物理实验数据可视化

运用MATLAB语言处理物理实验中的数据绘图问题。     

用MATLAB求解二元理想体系的泡露点问题

通过MATLAB工程计算软件，采用步长法、二分法、迭代法和黄金分割法等多种方法．求解了二元理想体系的泡露点问题．结果表明，几种计算值都能与手算值吻合地很好．相对误差远远小于1％，完全满足工程要求；用MATLAB内部函数Solve计算最为便捷．     

红外谱图计算机辅助检索系统的设计

介绍了红外光谱图谱计算机辅助检索系统中数据库的建立、谱图的编码、图库检索方法以及系统实现过程     

Efficient algorithms for the matrix cosine and sine

Several improvements are made to an algorithm of Higham and Smith for computing the matrix cosine. The original algorithm scales the matrix by a power of 2 to bring the ∞-norm to 1 or less, evaluates the [8/8] Padé approximant, then uses the double-angle formula cos (2A)=2cos ²A−I to recover the cosine of the original matrix. The first improvement is to phrase truncation error bounds in terms of ‖A²‖^1/2 instead of the (no smaller and potentially much larger quantity) ‖A‖. The second is to choose the degree of the Padé approximant to minimize the computational cost subject to achieving a desired truncation error. A third improvement is to use an absolute, rather than relative, error criterion in the choice of Padé approximant; this allows the use of higher degree approximants without worsening an a priori error bound. Our theory and experiments show that each of these modifications brings a reduction in computational cost. Moreover, because the modifications tend to reduce the number of double-angle steps they usually result in a more accurate computed cosine in floating point arithmetic. We also derive an algorithm for computing both cos (A) and sin (A), by adapting the ideas developed for the cosine and intertwining the cosine and sine double angle recurrences. AMS subject classification 65F30 Numerical Analysis Report 461, Manchester Centre for Computational Mathematics, February 2005. Gareth I. Hargreaves: This work was supported by an Engineering and Physical Sciences Research Council Ph.D. Studentship. Nicholas J. Higham: This work was supported by Engineering and Physical Sciences Research Council grant GR/T08739 and by a Royal Society–Wolfson Research Merit Award.     

基于遗传算法的非线性映射预测硝基苯化合物的生物毒性

摘要: 非线性映射是一种降维处理技术,通过Sammon算法可以将多维分析问题转化为二维问题分析。应用该法的关键在于寻求二维空间的最佳投影点,这可以转化为一个复杂的非线性优化问题来进行解决。遗传算法是解决各类函数优化和非线性映射问题的一种有效算法。以硝基苯化合物的生物毒性的模式识别为例,编制基于误差函数的目标函数和遗传算法约束参数,应用基于MATLAB的遗传算法工具箱进行优化求解。结果表明:该工具箱在求解此类非线性优化问题上是有效的, 基于遗传算法的非线性映射的预测结果比其它方法要好些。     

光纤通信中光孤子的传输特性分析

计算机模拟技术已经广泛应用在教学和科研中,在光纤通信课程教学中引入MATLAB语言,形象的给出光波在光纤中传输的模拟结果,既形象又深刻.以光孤子为例,给出基态孤子,二阶孤子和三阶孤子传输特性以及两个基态孤子的相互作用.     

MATLAB在物理实验CAI课件制作中的应用

介绍了MATLAB在物理实验CAI课件制作中常用的两种应用情况:在CAI课件中应用MATLAB软件和应用MATLAB GUI制作课件。将MATLAB制作的物理实验CAI课件引入教学,可以增加课件的交互能力,激发学生的学习兴趣,丰富实验教学内容,提高教学质量。     

Modelling and simulation of bicable ropeways under cross-wind influence

Improvements of safety standards of ropeways are crucial in order to ensure a high level of operational reliability and safety. In this context, the question of cross-wind stability of ropeways is of particular concern. The real cross-inclination of the gondola and its correlation to wind speed and direction on an operating ropeway are of great interest for ropeway manufacturers and responsible authorities as well as for ropeway operators. As presented in this paper, a mathematical model for simulation was developed in order to gain a better understanding of the cross-wind behaviour of bicable ropeways. This model was established for a numerical dynamic simulation of the movement of gondolas with stiff connections, ‘hanger-cabins’, due to arbitrary cross-wind loads acting at a section of the studied span of the ropeway. All equations were solved using the program MATLAB® and the toolbox SIMULINK®. In addition, the results of a simulation of a real ropeway are presented.     

城市表层土壤重金属污染风险等级评价

利用MATLAB软件编写程序作图,直观得到重金属污染元素Hg,Cu,Zn,Cr,Pb,Cd,Ni,As在不同区域(生活区、工业区、山区、主干道路、公园绿地区)的空间分布,并且对同一区域各种重金属的含量浓度作图,直观得出了各个区的污染情况.为了从理论上进行说明,利用单因子指数法计算出土壤中各项污染因子的含量,然后用尼梅罗综合污染指数法对不同区域的污染程度进行定量分析,得出生活区、工业区、山区、主干道路、公园绿地区的综合污染指数依次为(3.1706,13.1887,1.2735,9.3696,2.7003),从而确定了某城区重金属的主要污染源.以此能够更为科学、综合的评价该区域内总体土壤质量状况.