WU Zhenxiang,CHEN Liang*,ZHOU Tong.A new modified Levenberg -Marquardt method for systems of nonlinear equations[J].Journal of Yanbian University,2020,46(04):302-307,332.
一种改进的求解非线性方程组的Levenberg -Marquardt方法
- Title:
- A new modified Levenberg -Marquardt method for systems of nonlinear equations
- 文章编号:
- 1004-4353(2020)04-0302-07
- 关键词:
- 非线性方程组; 局部误差界; 二次收敛; Levenberg -Marquardt
- Keywords:
- systems of nonlinear equations; local error bound condition; local convergence; Levenberg -Marquardt
- 分类号:
- O221.1
- 文献标志码:
- A
- 摘要:
- 通过修改Levenberg -Marquardt参数,得到了一种改进的求解非线性方程组的Levenberg -Marquardt算法.利用信赖域技术,在不必假设雅克比矩阵非奇异的局部误差界条件下,证明了该算法至少具有超线性收敛性.数值实验表明,该算法能有效求解非线性方程组问题.
- Abstract:
- By modifying the Levenberg -Marquardt parameters, we obtain a new convergent Levenberg -Marquardt algorithm for solving the systems of nonlinear equations. By using trust region technique, under the condition of local error bounds, the convergence of the new Levenberg -Marquardt method is shown to be at least super linearly without the non -singularity assumption of the Jacobi matrix. Numerical experiments show that the new algorithm can solve nonlinear equations effectively.
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备注/Memo
收稿日期: 2020-09-28 *通信作者: 陈亮(1977—),男,博士,教授,研究方向为数值最优化和数值代数.
基金项目: 安徽省高校优秀青年骨干人才国外访问研修项目(GXGWFX2019022); 安徽省高校自然科学研究项目(KJ2020ZD008,KJ2019A0604); 安徽省省级质量工程项目(2019MOOC158)