一种求解非线性方程组的多步Levenberg-Marquardt算法  

A Multi-Step Levenberg-Marquardt Algorithm for Solving Systems of Nonlinear Equations

作　　者：司京宇 芮绍平[1] 安梦瑶 SI Jingyu;RUI Shaoping;AN Mengyao(College of Mathematics,Huaibei Normal University,Huaibei 235000,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《长春师范大学学报》2025年第2期16-21,共6页Journal of Changchun Normal University

基　　金：安徽省教育厅自然科学研究项目“大规模无约束优化问题的非精确非单调算法及其应用研究”(2023AH050348)。

摘　　要：根据Levenberg-Marquardt算法,结合解非线性方程的King算法的思想,提出一种解非线性方程组的三步迭代算法.在局部误差界条件下进行收敛性分析,证明了该算法的全局收敛性及局部四阶收敛性.数值实验结果表明,该算法稳定有效,更有优势.Based on the Levenberg-Marquardt algorithm and incorporating the concept of King s algorithm for solving nonlinear equations,a three-step iterative algorithm for solving nonlinear systems of equations is proposed.Convergence analysis is conducted under the condition of local error bounds,demonstrating the global convergence and local fourth-order convergence of the algorithm.Numerical experimental results indicate that the algorithm is stable,effective,and possesses superior advantages.

关 键 词：LEVENBERG-MARQUARDT算法 King算法 非线性方程组 

分 类 号：O221.1[理学—运筹学与控制论]