69数值分析论文

课程论文任务书学生姓名指导教师论文题目数值分析课程设计论文内容（需明确列出研究的问题）：本文主要描述运用数值分析的知识来解决数学研究问题中的计算问题，包括运用拉格朗日插值公式以及牛顿插值公式来根据观测点来构造一个反应函数的特征并计算未观测到点的函数值、运用最小二乘法确定系数以及列主元Gauss消去法求解方程组。资料、数据、技术水平等方面的要求：论文要符合一般学术论文的写作规范，具备学术性、科学性和一定的创造性。文字要流畅、语言要准确、论点要清楚、论据要准确、论证要完整、严密，有独立的观点和见解。内容要理论联系实际，计算数据要求准确，涉及到他人的观点、统计数据或计算公式等要标明出处，结论要写的概括简短。参考文献的书写按论文中引用的先后顺序连续编码。发出任务书日期完成论文（设计）日期学科组或教研室意见（签字）院、系（系）主任意见（签字）Ⅱ目录【摘要】....................................................................................................................................................Ⅰ【关键词】...................................................................................................................................................ⅠAbstract.........................................................................................................................................................ⅡKeywords......................................................................................................................................................Ⅱ一、插值问题与插值多项式.......................................................................................................................1（一）基础知识.....................................................................................................................................1（二）题目：.........................................................................................................................................2（三）程序清单：.................................................................................................................................5（四）实验结果分析：.........................................................................................................................7二、最小二乘法.............................................................................................................................................7（一）基础知识.....................................................................................................................................7（二）题目：.........................................................................................................................................8（三）程序清单：.................................................................................................................................9（四）实验结果分析：.......................................................................................................................10三、列主元Gauss消去法......................................................................................................................11（一）基础知识...................................................................................................................................11（二）题目...........................................................................................................................................12（三）程序清单：...............................................................................................................................12（四）实验结果分析：.......................................................................................................................13四、实验心得：...........................................................................................................................................14I数值分析课程设计【摘要】数值分析是研究各种数学问题求解的数值计算方法，是数学中计算数学分支的重要内容。近几十年来，随着计算机的飞速发展，数值计算方法的学习与研究越来越离不开计算机。实际计算中遇到的数值问题只有与计算机相结合，算法与程序密切联系，形成切实可靠的数值软件才能为社会创造更大的社会财富。本文主要描述运用数值分析的知识来解决数学研究问题中的计算问题，包括运用拉格朗日插值公式以及牛顿插值公式来根据观测点来构造一个反应函数的特征并计算未观测到点的函数值、运用最小二乘法确定系数以及列主元Gauss消去法求解方程组。【关键词】插值问题与插值多项式最小二乘法列主元Gauss消去法IICourseDesignforNumericalAnalysisAbstractNumericalanalysisisanimportantbranchofmathematics,whichoffersvariousmumericalmethodstosolvemathematicalproblemsolving.Inrecentdecades,withtherapiddevelopmentofcomputers,,numericalmethodsoflearningandresearchareincreasinglyinseparablefromthecomputer.Actualnumericalproblemsencounteredinthecalculationonlycombinedwiththecomputer,aswellasalgorithmsandprocedurescontactedcloselyinordertoformapracticalandreliablenumericalsoftware,canitcreateagreatofsocialwealth.Thispaperusenumericalanalysisofmathematicalknowledgetosolveresearchproblemsandcomputationalproblems,includingbyusingcolumnpivotgausseliminationmethodforthesolutionofequations,Newton'siterativemethodforfindingtherootofaequation；IncludingusingLagrangeinterpolationformulaandtheNewtoninterpolationformulatoaccordingtothecharacteristicsoftheobservationpointtoconstructaresponsefunctionnotobservationtopointandcalculatethefunctionvalue,usingtheleastsquaresmethodtodeterminecoefficient,andcolumnpcaGausseliminationmethodofsolvingequations.KeywordsWiththeinterpolationpolynomialinterpolationproblemTheleastsquaremethodColumnpcaGausseliminationmethod1一、插值问题与y=f(x)插值多项式（一）基础知识定义1设为区间],[ba上y=f(x)函数，nxxx,,,10为],[ba上1n互不相同的点，为给定的某一函数类，若上有函数)(x，满足nixfxii,,2,1,0),()(.(1)则称)(x为)(xf关于节点nxxx,,,10在上的插值函数，称点nxxx,,,10为插值节点；称nixfxii,,2,1,0),(,(为插值型值点，简称型值点或插值点;)(xf称为被插函数.定义2已知函数)(xf在区间],[ba上的1n个点的值，即已知],[baxi，寻求一个解析形式的函数)(x，使之满足,)(iiyxni,,2,1,0(2)则称ix为插值结点,)(xf为被插值函数，)(x为插值