一种求解非线性方程组的有效Levenberg-Marquardt算法  

An Effective Levenberg-Marquardt Algorithm for Solving Systems of Nonlinear Equations

作　　者：韩扬 芮绍平[1] HAN Yang;RUI Shao-ping(School of Mathematical Sciences,Huaibei Normal University,Huaibei 235000,China)

机构地区：[1]淮北师范大学数学科学学院,淮北235000

出　　处：《青岛大学学报（自然科学版）》2024年第2期3-9,21,共8页Journal of Qingdao University(Natural Science Edition)

基　　金：安徽省教育厅自然科学研究项目(批准号:2023AH050348,2023ZK027,2023ZK030)资助。

摘　　要：通过修改LM参数,并结合非单调技术和信赖域技术给出一种求解非线性方程组的有效Levenberg-Marquardt算法,即AMLM算法。在局部误差界条件下,证明了AMLM算法具有局部快速收敛性。数值实验结果表明,AMLM算法稳定、有效。A new effective Levenberg-Marquardt algorithm for solving systems of nonlinear equations,namely AMLM algorithm was presented by modifying LM parameters,combining nonmonotone technique and trust region technique.The local fast convergence of the AMLM algorithm was proved under the local error bound condition.Numerical results show that the AMLM algorithm is stable and effective.

关 键 词：LM参数 非单调技术 信赖域技术 LEVENBERG-MARQUARDT算法 

分 类 号：O221.1[理学—运筹学与控制论]