用MATLAB解决高等数学中的图形问题

本文通过实例将 MATLAB与 Mathematica的图形功能做了比较 ,指出了 MATLAB在解决高等数学图形问题时的优势 .     

慕课背景下MATLAB与线性代数应用的融合——介绍国家精品在线开放课程“实用大众线性代数(MATLAB版)”

本文介绍了国家精品在线开放课程"实用大众线性代数(MATLAB版)",该课程具有科学的知识体系,拥有大量的应用实例,并把MATLAB与应用实例深度融合,学以致用.     

模糊线性规划在大学生最低饮食支出问题中的应用

如何用最小的饮食支出来满足自身的营养需求是很多大学生关心的问题。本文以上海海事大学为例,通过对食堂58种主副食所含营养元素的统计分析,结合人体每天所需营养元素及其数量等约束条件,建立了模糊线性规划模型,借助MATLAB软件分别求解出男生和女生每天最低的饮食支出及相应的食谱。此外,针对未进行模糊处理的线性规划模型,本文还给出了关于营养元素和菜品价格的灵敏度分析,并在此基础上给食堂经营者提出若干优化建议。     

基于MATLAB打造高中数学灵动课堂

随着互联网、人工智能技术的快速发展,MATLAB的应用越来越广泛.本文分析了传统高中数学教学中的不足,并提出使用MATLAB打造高中数学灵动课堂.在使用MATLAB对高中数学做计算分析时发现,MATLAB不仅能生动形象的绘制各种复杂函数,而且对模拟逼近计算有着非常出色的表现,能在一定程度上使得课堂变得更加灵动、更有趣味.     

利用MATLAB进行高等数学的辅助教学

探讨了利用MATLAB的绘图和动画制作功能进行高等数学的辅助教学,列举了MATLAB的绘图功能在教学中的一些应用,给出了制作旋转曲面、柱面形成动画的程序代码.     

多目标优化配气数学模型及其MATLAB编程实现

为了更全面地理解区块优化配气问题,更快速深入地掌握区块优化配气方法,将详尽的数学模型及其MATLAB代码同时给出.采用高次多项式拟合得到目标函数,根据产量、经济效益、混合目标三种需求,结合现场主要考虑的四种约束条件,建立了全面而详尽的三类数学模型.给出了求解模型最关键的四个MATLAB函数文件,并与其数学模型一一对应.求解得到了三类模型在不同约束状态下的配气方案,并与现场常用的简易配气方法进行比较,最后给出了一种充分利用各类设备处理能力的方法.     

儿童主体性发展中教师与家长对幼儿评价的统计分析

儿童主体性发展中教师与家长对幼儿评价的统计分析．本文应用典型相关分析方法,对幼儿主体性发展进行统计分析,通过北京师范大学收集的教师和家长对幼儿评价的抽样调查数据,分析了幼儿在家与在园中主体性表现的差异和联系,为制订教育措施提供可靠的依据     

一种组合数矩阵及其性质

构造了一个对称正定矩阵,矩阵元素与组合数有关,讨论了该矩阵的一些性质.根据MATLAB数值计算的结果,提出了该矩阵有关特征值性质的一些猜想.     

一种组合数矩阵及其性质

构造了一个对称正定矩阵,矩阵元素与组合数有关,讨论了该矩阵的一些性质.根据MATLAB数值计算的结果,提出了该矩阵有关特征值性质的一些猜想.     

CT系统参数标定及成像的数学模型

本文首先借助MATLAB软件对CT扫描的接受信息进行拟合,得出一系列关于CT系统参数标定及成像的图像.然后通过对接受信息与图像的综合处理,建立了CT系统参数的标定模型与介质在CT系统中的成像模型.     

Algorithms for range restricted iterative methods for linear discrete ill-posed problems

Range restricted iterative methods based on the Arnoldi process are attractive for the solution of large nonsymmetric linear discrete ill-posed problems with error-contaminated data (right-hand side). Several derivations of this type of iterative methods are compared in Neuman et al. (Linear Algebra Appl. in press). We describe MATLAB codes for the best of these implementations. MATLAB codes for range restricted iterative methods for symmetric linear discrete ill-posed problems are also presented.     

求解第一类Fredholm积分方程的一种新的正则化算法

应用一种新的正则化方法建立了一类新的求解第一类Fredholm积分方程的正则化算法, 并借助Matlab软件给出了数值算例.数值结果与理论分析基本一致,而且表明文中建立的正则化比通常的Tikhonov正则化更精确.     

基于MTALAB的神经网络判别模型

判别分析是判别样品所属类型的一种统计方法.利用M ATLAB提供的神经网络工具箱为基础,设计了一个三层BP神经网络判别模型,提出了一种进行判别分析的新方法,实例表明,利用BP神经网络建立的判别模型是进行判别分析的有效方法.是对研究分类问题的方法的扩充.     

Efficient orthogonal matrix polynomial based method for computing matrix exponential

The matrix exponential plays a fundamental role in the solution of differential systems which appear in different science fields. This paper presents an efficient method for computing matrix exponentials based on Hermite matrix polynomial expansions. Hermite series truncation together with scaling and squaring and the application of floating point arithmetic bounds to the intermediate results provide excellent accuracy results compared with the best acknowledged computational methods. A backward-error analysis of the approximation in exact arithmetic is given. This analysis is used to provide a theoretical estimate for the optimal scaling of matrices. Two algorithms based on this method have been implemented as MATLAB functions. They have been compared with MATLAB functions funm and expm obtaining greater accuracy in the majority of tests. A careful cost comparison analysis with expm is provided showing that the proposed algorithms have lower maximum cost for some matrix norm intervals. Numerical tests show that the application of floating point arithmetic bounds to the intermediate results may reduce considerably computational costs, reaching in numerical tests relative higher average costs than expm of only 4.43% for the final Hermite selected order, and obtaining better accuracy results in the 77.36% of the test matrices. The MATLAB implementation of the best Hermite matrix polynomial based algorithm has been made available online.     

IR Tools: a MATLAB package of iterative regularization methods and large-scale test problems

Numerical Algorithms - This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called...     

SimHPN: A MATLAB toolbox for simulation, analysis and design with hybrid Petri nets

This paper presents a MATLAB embedded package for hybrid Petri nets called SimHPN. It offers a collection of tools devoted to simulation, analysis and synthesis of dynamical systems modeled by hybrid Petri nets. The package supports several server semantics for the firing of both, discrete and continuous, types of transitions. Besides providing different simulation options, SimHPN offers the possibility of computing steady state throughput bounds for continuous nets. For such a class of nets, optimal control and observability algorithms are also implemented. The package is fully integrated in MATLAB which allows the creation of powerful algebraic, statistical and graphical instruments that exploit the routines available in MATLAB.     

确定高精度参数问题

在航天器精确制导等高科技的实际问题中,必须高精度地估计模型中的大批参数,建立高精度的数学模型,考虑较简单的确定高精度参数问题:食饵-捕食者系统.对于绝大多数微分方程得不到解析解,尤其是非线性微分方程这样的情况,运用稳定性理论和常微分方程几何理论来分析该生态模型.在数据分析处理中,采用了大量优化算法,如灰色系统辩识方法,多项式曲线选阶及拟合算法,牛顿迭代法等等.最后,通过MATLAB仿真验证了本方法的可行性.     

Sampling of Bandlimited Functions on Unions of Shifted Lattices

We consider Shannon sampling theory for sampling sets which are unions of shifted lattices. These sets are not necessarily periodic. A function f can be reconstructed from its samples provided the sampling set and the support of the Fourier transform of f satisfy certain compatibility conditions. An explicit reconstruction formula is given for sampling sets which are unions of two shifted lattices. While explicit formulas for unions of more than two lattices are possible, it is more convenient to use a recursive algorithm. The analysis is presented in the general framework of locally compact abelian groups, but several specific examples are given, including a numerical example implemented in MATLAB. Our methods also provide a new tool for designing sampling sets of minimal density.     

Dynamics of a Predator-Prey Model with Allee Effect and Herd Behavior

This paper deals with dynamics of a predator-prey model with Allee effect and herd behavior. We first study the stability of non-negative constant solutions for such system. We also establish the existence of Hopf bifurcation solutions for such predator-prey model. The stability and bifurcation direction of Hopf bifurcation solution in the case of spatial homogeneity are further discussed. At the same time, several examples are given by MATLAB. Finally, the numerical simulations of the system are carried out through MATLAB, which intuitively verifies and supplements the theoretical analysis results.     

瞬态热传导的奇异边界法及其MATLAB实现

基于动力学问题时间依赖基本解的奇异边界法是一种无网格边界配点法.该方法引入源点强度因子的概念从而避免了基本解的源点奇异性,具有数学简单、编程容易、精度高等优点.将该方法用于瞬态热传导问题的数值模拟,运用MATLAB实现该问题的数值研究,并创建相应的MATLAB工具箱.针对二维和三维瞬态热传导问题,进行了基于反插值技术和经验公式的奇异边界法MATLAB算例实现.针对支撑圆坯低温瞬态温度场的模拟结果表明,瞬态热传导奇异边界法的MATLAB工具箱具有简单、方便、精确可靠的优点.研究成果有助于发展瞬态热传导的奇异边界法,并为瞬态热传导问题的数值分析和仿真提供了一种简单高效的模拟工具.