求解非线性方程组地几种迭代方法的理论及应用案例摘要 随着人类文明的不断发展，科学技术的不断进步，数值计算一直在帮助人们解决各类生活与工作问题。用迭代法求解非线性方程组是数值计算中重要的研究内容，也是科学计算和计算数学的核心问题，它在国防、科技、经济、工程、管理等许多领域有着广泛的应用。因此，研究非线性方程组的各种迭代方法具有非常重要的理论意义和实际价值。本文主要介绍几种迭代法来求解非线性方程组，主要以牛顿迭代法为主，再加上它的一些改进后的迭代方法。利用C语言编程来模拟几种迭代方法，得到它们的近似解和迭代次数。在求解非线性方程组的过程中，预先设置的初值和误差精度是非常重要的，它们能直接影响所求的解的可信程度。用C语言编程的方法能更好的帮助人们了解迭代法求解非线性方程组的过程与结果，为数值分析提供了良好的环境，让学者更好的研究改善迭代方法。对牛顿迭代法及其一些改进方法通过算例进行了比较，得出当所给初值最接近精确解时，牛顿弦截法计算效率最高，收敛速度最快。再牛顿迭代法与不动点迭代法的比较算例中，不动点迭代法的计算效率与收敛速度更高。关键词 数值分析 非线性方程组 迭代方法 迭代次数 C语言编程ITheory and application cases of several iterative methods for solving nonlinear equationsAbstract With the continuous development of human civilization, science and technology, numerical calculation has been helping people to solve all kinds of life and work problems. It is not only important research content in numerical calculation, but also the core problem of scientific calculation and computational mathematics to solve nonlinear equations by iterative method. It has a wide range of applications in many fields, such as national defense, science and technology, economy, engineering, management and so on. Therefore, it is of great theoretical and practical significance to study various iterative methods of nonlinear equations.This paper mainly introduces several iterative methods to solve nonlinear equations, mainly Newton iterative method, plus some of its im...
