非线性方程组解法的研究与应用.docxVIP

PAGE 18 摘要 在研究自然现象和社会问题时数学是一种重要的工具，科技飞速发展，电子计算机已然成为大众生活的必需品，电子信息技术可谓大放异彩，也因此非线性问题成为数值计算领域的重要研究方向之一，而即将要讨论的非线性方程组的求解的相关问题则是其中最基本的问题。实际上，在工程实践、经济模拟、系统研发以及信息安全等许多方面，我们都可以看到大量的实际问题最终转化成为非线性方程组的求解问题。随着生活质量的不断提高，也导致要解决的问题越来越庞大，越来越复杂，却也促进了非线性方程组求解的发展，其研究具有非常高的实用价值。近年来，国内外学者围绕这一主题进行深入研究，主要集中在牛顿法、高阶收敛法以及人工智能算法等方面。 本文对非线性方程组解法的有关观点加以阐明，沿着本文论题这条主线，对研究过程中可能出现的数学方法方面的问题做了相应的分析。本文通过参考文献著作归纳整理了部分基础和较为高效的求解算法。而在相应的应用方面，主要集中在科学技术、化学工程、数值计算等方面，以航空发动机、水利系统中非线性方程组的应用为例进行论述。 关键词：非线性方程组求解；牛顿法；单纯形算法；遗传算法 Abstract In the study of natural phenomena and social problems in mathematics is a kind of important tool, the rapid development of science and technology, the electronic computer has become a mass of the necessities of life, the electronic information technology is to shine, and the problem of nonlinear becomes one of the important research direction in the field of numerical calculation, and the problem of solving the nonlinear equations is the most basic one. In fact, in many aspects such as engineering practice, economic simulation, system research and development, and information security, we can see that a large number of practical problems are finally transformed into the solution of nonlinear equations. With the continuous improvement of the quality of life, the problems to be solved become larger and more complex, but also promote the development of the solution of nonlinear equations, its research has a very high practical value. In recent years, scholars at home and abroad have conducted in-depth research on this topic, mainly focusing on Newton method, high-order convergence method and artificial intelligence algorithm. In this paper, the views of the method of solving nonlinear equations are expounded, and the possible problems of mathematical methods in the research process are analyzed along the main line of the thesis.In this paper, some basic and efficient algorithms are summarized by reference works. The corresponding applications are mainly focused on science and tech