51基于matlab的数值逼近仿真设计与实现

西南科技大学本科生毕业论文I基于Matlab的数值逼近算法仿真设计与实现摘要：数值计算方法是计算机及相关专业的重要基础理论之一，是程序设计和软件开发的基础。Matlab是当前最为优秀的科学计算软件之一，也是许多科学领域中分析、应用和开发的基本工具。经过多年的发展，Matlab已经成为一种功能全面的软件，几乎可以解决科学计算中的所有问题。由于其编写简单，代码效率高，Matlab广泛应用于计算机通信、信号处理、数值计算等领域。Matlab是一种面向科学与工程计算的高级语言，它提供了强大的矩阵处理和绘图功能，给出了一个融合计算、可视化和程序设计的交互环境，操作简便。本设计以Matlab为编程语言和开发环境，对数值逼近算法进行编程实现，并进行图形化描述。所有结果表明，采用不同的逼近方法，利用Matlab编程可以简单、有效地实现函数逼近。关键词：Matlab；函数逼近；拉格朗日插值；曲线拟合西南科技大学本科生毕业论文IIDesignandRealizationofnumericalApproximationalgorithmbasedonMatlabAbstract:Numericalcalculationmethodisabasictheoryofprofessionalcomputerandrelated,itisabasicofprogrammingandsoftwaredevelopment.Matlabisoneofthemostoutstandingscientificcalculationsoftware,butalsoismanyscienceanalysis,applicationanddevelopmentofthebasictools.Afteryearsofdevelopment,Matlabhasbecomefullyfunctionalsoftware;itcansolvealmostallproblemsinscientificcomputing.Duetoitssimplepreparation,highefficiency,Matlabiswidelyappliedinthecomputercommunication,signalprocessing,numericalcalculationandotherareas.Matlabisorientedtoscienceandengineeringcalculationofhigh-levellanguage;itprovidesstrongmatrixprocessinganddrawingfunctions,givesafusioncalculation,visualizationandtheprogramdesignoftheinteractiveenvironment,simpleoperation.ThedesignuseMatlabasprogramminglanguageanddevelopmentenvironment,thenumericalapproximationalgorithmforprogramming,andagraphicaldescription.Alltheresultsshowthat,usingdifferentapproximationmethods,theuseofMatlabprogrammingcanbesimple,effectiverealizationoffunctionapproximation.Keywords:Matlab,functionapproximation,Lagrangeinterpolation,curvefitting西南科技大学本科生毕业论文III目录第1章绪论.......................................................11.1背景......................................................11.1.1Matlab的发展........................................11.1.2数值逼近............................................21.1.3研究意义............................................31.2论文结构................................................3第2章MATLAB简介.................................................42.1基本功能..................................................42.2基本应用..................................................52.3系统结构..................................................62.3.1MATLAB开发环境.......................................62.3.2MATLAB数学函数库.....................................72.3.3MATLAB语言...........................................72.3.4MATLAB图形处理系统...................................72.3.5MATLAB应用程序接口...................................72.4特点与优势................................................82.4.1特点.................................................82.4.2优势.................................................8第3章数值逼近...................................................123.1数值拟合..................................................123.1.1直线拟合............................................133.1.2曲线拟合............................................153.1.3多项式拟合..........................................153.2插值逼近..................................................163.2.1定义与发展..........................................163.2.2主要内涵............................................163.2.3基本类型............................................17第4章基于matlab的数值逼近程序设计..............................19西南科技大学本科生毕业论文IV4.1分段插值..................................................194.1.1定义................................................194.1.2分段插值计算........................................204.1.3基于matlab分段插值实现.............................204.1.4小结................................................214.2拉格朗日插值..............................................214.2.1线性插值............................................214.2.2二次朗格拉日插值....................................234.2.3n次拉格朗日插值.....................................244.2.4拉格朗日计算........................................264.2.5基于matlab的拉格朗日程序设计.......................264.2.6rung（龙格）现象....................................274.3三次样条插值..............................................294.3.1定义................................................294.3.2三次样条插值计算....................................304.3.3基于matlab三次样条插值实现.........................314.3.4小结................................................324.4拟合......................................................334.4.1定义................................................334.4.2基于matlab的拟合的实现.............................334.4.4小结................................................354.5各类逼近方式解决实际问题...................................35第5章基于matlab的数值逼近程序测试..............................385.1插值逼近程序测试..........................................385.2拟合程序测试..............................................415.3各种逼近应用..............................................42结论............................................................45致谢............................................................46参考文献..........................................................47西南科技大学本科生毕业论文1第1章绪论在工程分析和科学研究中，常需要根据一些测试数据求得自变量和因变量的近似函数关系式．来完成其他设计计算。这就要求用简单的函数(z)近似地代替函数厂(z)，这种近似代替称为函数逼近，它是计算数学中最基本的概念和方法之一，在图像处理、逆向工程以及测试数据的处理等领域应用得相当广泛。函数逼近的方法包括插值、拟合与逼近，这些算法可以通过C，C++以及Fortran等语言编程实现．但是计算过程都比较复杂。Matlab是一种面