摘要
Levenberg-Marquardt方法是求解非线性方程组的重要算法之一,在本文中,我们针对奇异非线性方程组给出了Levenberg-Marquardt方法的一种新的参数迭代方法,即取μk=||J(xk)TF(xk)||.我们证明了在弱于非奇异性条件的局部误差有界下,Levenberg-Marquardt方法仍具有局部二次收敛速度.数值实验表明算法是很有效的.
Levenberg-Marquardt method is one of the most important methods for solving systems of nonlinear equations. In this paper, we consider the convergence of a new Levenberg-Marquardt method (i.e.μk = || J(xk)TF(xk)||) for solving a system of singular nonlinear equations F(x) = 0, where F is a mapping from Rn into Rm. We will show that if ||F(x)|| provides a local error bound which is weaker than the condition of nonsingularity for the system of nonlinear equations, the sequence generated by the new Levenberg-Marquardt method converges to a point of the solution set X* quadratically. Numerical experiments and comparisons are reported.
出处
《计算数学》
CSCD
北大核心
2005年第1期55-62,共8页
Mathematica Numerica Sinica
基金
"新世纪优秀人才支持计划"项目国家自科基金项目教育部和湖南省教育厅重点项目湖南省教育厅科研项目(03C453)资助.
