全不确定线性系统及方法

发布时间：2018-03-06 00:08

本文选题：不确定变量　切入点：系数矩阵　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着科学和工程技术的发展,线性代数中一般形式的线性系统已经无法达到研究应用的要求,变量为不确定的线性系统得到了众人的关注。李波和朱元国教授于2014年提出了不确定线性系统的概念,并给出了相关求解公式。本文在此基础上提出了全不确定线性系统(或全不确定线性方程)的概念,并定义了全不确定线性系统的解。随后,文章讨论了全不确定线性系统有解的充分条件。针对系统系数矩阵为方阵和非方阵的情况,本文分别给出了系统的求解公式以及系统有解的判断条件。考虑到求解时需要求矩阵逆,当系数矩阵维数较大时其计算量非常大,不便于应用,因此,本文进一步讨论了关于全不确定线性系统的数值迭代算法求解,并分析了几种迭代法在求解全不确定线性系统时其迭代格式的收敛性问题。最后,文章给出了关于全不确定线性系统的几个数值例子和一个应用实例。
[Abstract]:With the development of science and engineering technology, the general form of linear system in linear algebra has been unable to meet the requirements of research and application. In 2014, Professor Li Bo and Professor Zhu Yuanguo put forward the concept of uncertain linear system. In this paper, the concept of fully uncertain linear systems (or fully uncertain linear equations) is proposed, and the solution of fully uncertain linear systems is defined. In this paper, the sufficient conditions for the existence of solutions for fully uncertain linear systems are discussed. In this paper, the solution formulas of the system and the judgment conditions of the solution are given respectively. Considering that the inverse matrix needs to be solved, when the dimension of the coefficient matrix is large, the calculation is very large and is not easy to be applied. In this paper, we further discuss the numerical iterative algorithm for solving fully uncertain linear systems, and analyze the convergence of the iterative schemes of several iterative methods for solving fully uncertain linear systems. In this paper, several numerical examples and an application example of fully uncertain linear systems are given.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.2

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