目录摘要...............................................................11前言.............................................................32直接法简介.......................................................42.1Gauss消去法.................................................42.1.1实例..................................................42.1.2Gauss消去法的运算量....................................52.1.3Gauss消去法能够进行下去的条件..........................52.2列主元Gauss消去法...........................................62.2.1实例...................................................72.2.2列主元Gauss消去法的运算量..............................72.3全主元Gauss消去法...........................................72.3.1实例...................................................82.3.2全主元Gauss消去法的运算量..............................82.4平方根法....................................................82.4.1实例...................................................92.4.2平方根法的运算量......................................102.5改进的平方根法.............................................102.5.1实例..................................................102.5.2改进的平方根法的运算量................................112.6追赶法.....................................................112.6.1实例..................................................122.6.2追赶法的运算量........................................123直接法的误差分析................................................133.1线性方程组的敏感性和条件数.................................133.2误差分析...................................................154数值算例........................................................164.1算例1.....................................................164.2算例2.....................................................164.3算例3.....................................................174.4算例4.....................................................175总结............................................................18参考文献..........................................................19致谢..............................................................20摘要本文采用Matlab软件计算，介绍了解线性方程组常用的几种直接法：Gauss消去法、列主元Gauss消去法、全主元Gauss消去法、平方根法、改进的平方根法、追赶法，及其的基本思想、解题实例和运算量；并对直接法进行了误差分析；最后通过数值算例比较前五种直接法的误差，讨论其适用矩阵及其差异。关键词：线性方程组，Gauss，平方根法，误差分析。AbstractInthispaper,Matlabsoftwareisusedtocalculateandintroduceseveralcommondirectmethodsforsolvinglinearequations:Gausseliminationmethod,ColumnprincipalelementGausselimination,FullPrincipalComponentGaussElimination,Squarerootmethod,Improvedsquarerootmethod,Chasingmethodandtheirbasicideas,problemsolvingexamples,andcomputationalload.Anderroranalysisofthedirectmethod.Finally,theerrorsofthefirstfivedirectmethodsarecomparedbynumericalexamples,andtheapplicablematrixanditsdifferencesarediscussed.Keywords:Linearequations,Gauss,Squarerootmethod,Erroranalysis.1前言在自然科学和工程计算的领域中，很多问题往往可以归结为解线性代数方程组。而这些问题可以归为两张类型，一种是各种实际的应用问题，例如电学网络问题，船体数学放样问题，电磁场数值计算问题等；另一种是数学研究问题，例如求解非线性方程组，微偏分方程的边值问题，差分法求解常微分方程等。n阶线性方程组，即其中，是方程组的系数矩阵，这些方程组的一般可分为两类：低阶稠...
