线性方程组的解法讨论论文.doc

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本科生毕业论文
论文题目:线性方程组的解法讨论
作者、学号：XXX
学院、年级：数学与信息科学学院2021级
学科、专业：数学与应用数学
指导教师：XXXX
完成日期：2021年5月20日
师学院教务处
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线性方程组的解法讨论
摘 要
科学技术、工程和经济领域中的一些实际问题建立数学模型时通常可以与线性方程组对应起来，因此，AX=，针对齐次线性方程组和非齐次线性方程组，结合例题讨论了它们的解法，主要有高斯消元法、克拉姆法、LU分解法、逆矩阵及广义逆矩阵法，并对每种方法的优缺点及适用性进展了分析，得出线性方程组的解法虽多，但要根据线性方程组的构造选择适宜的方法，方能顺利求解的结论.
关键词 ：线性方程组；高斯消元法；克拉姆法那么；LU分解法；逆矩阵法
Discussion about the Solution of Linear System of Equations
Abstract:Some practical problems of science and technology, engineering and economic areas of the mathematical model can usually correspond to linear equations, and therefore, the solution of AX=b is a central problem in scientific puting. This paper introduces the concept and the basic theory of linear equations solution, according to the system of homogeneous linear equations and nonhomogeneous linear equations bined with the example, discusses their solution, mainly Gauss elimination method, LU deposition method, Crum method, inverse matrix and generalized inverse matrix method, and the advantages and disadvantages of each method and applicability are analyzed, that although the solution of linear equations, but to choose the appropriate method according to the linear equation the form of a group, can be solved smoothly conclusions.
Keywords: linear System of equations； Gauss elimination method；Cra