求解非线性方程组的信赖域算法  

Trust Region Algorithm for Solving Nonlinear Equations

作　　者：唐江花[1] TANG Jianghua(Department of General Education,Anhui Xinhua University,Hefei 230088,China)

机构地区：[1]安徽新华学院通识教育部,安徽合肥230088

出　　处：《吉林化工学院学报》2021年第5期85-89,共5页Journal of Jilin Institute of Chemical Technology

摘　　要：非线性方程组传统解法求解过程中迭代次数多、运算时间长,因此提出一种求解非线性方程组的信赖域算法.首先建立信赖域算法模型,将非线性方程组转化为无约束问题,确定迭代过程参数,建立Hessian阵并构造近似序列,随后利用反证法进行收敛性分析,验证算法可行性.仿真实验中选择3个案例对与传统算法进行比较验证,实验结果表明,两算法得到的求解结果相似,但在计算中的迭代次数、CPU时间和函数值等参数值均优于传统算法.The traditional method of solving nonlinear equations has many iterations and takes a long time.Therefore,a trust region algorithm for solving nonlinear equations is proposed.Firstly,the trust region algorithm model is established,the nonlinear equations are transformed into unconstrained problems,the iterative process parameters are determined,the Hessian matrix is established,and the approximate sequence is constructed.Then,the convergence analysis is carried out by using the counter argument method to verify the feasibility of the algorithm.In the simulation experiment,three cases are selected to verify the traditional algorithm and the algorithm proposed in this paper.The experimental results show that the results of the two algorithms are similar,but the iteration times,CPU time and function value are better than the traditional algorithm.

关 键 词：非线性方程组 信赖域算法 收敛性分析 无约束问题 迭代过程参数 

分 类 号：O241.7[理学—计算数学]