求解非线性方程组的几种迭代方法的理论及应用案例

Theory and application cases of several iterative methods for solvingnonlinear equationsAbstract With the continuous development of human civilization,science andtechnology,numerical calculation has been helping people to solve all kinds of life andwork problems.It is not only important research content in numerical calculation,but alsothe core problem of scientific calculation and computational mathematics to solvenonlinear equations by iterative method.It has a wide range of applications in many fields,such as national defense,science and technology,economy,engineering,managementand so on.Therefore,it is of great theoretical and practical significance to study variousiterative methods of nonlinear equations.This paper mainly introduces several iterative methods to solve nonlinear equations,mainly Newton iterative method,plus some of its improved iterative methods.C languageis used to simulate several iterative methods,and their approximate solutions and iterativetimes are obtained.In the process of solving nonlinear equations,the pre-set initial valueand error accuracy are very important.They can directly affect the reliability of the solution.The method programmed by C language can help people better understand the processand results of solving nonlinear equations by iterative method,provide a goodenvironment for numerical analysis,and make scholars better study and improve theiterative method.By comparing the Newton iterative method and some improved methods,it is concluded that the Newton chord section method has the highest efficiency and thefastest convergence speed when the given initial value is closest to the exact solution.Compared with the fixed point iteration method,the fixed point iteration method has higherefficiency and convergence rate.Key words numerical analysis,nonlinear equations,iterative method,number ofiterations,C language programming