摘要
在文献[1]的基础上,结合信赖域技术和Levenberg-Marquardt方法求解非线性方程组的特点,提出了一种求解奇异非线性方程组的修正的Levenberg-Marquardt方法,给出了算法的全局收敛性,并在弱于非奇异条件的局部误差有界的条件下,证明了修正的Levenberg-Marquardt方法仍具有局部二阶收敛速度,数值试验表明算法是非常有效的。
Based on the work of paper[1], a modified Levenberg-Marquardt method for solving systems of singular nonlinear equations is presented by combining the trust-region techniques with the characteristic of the Levenberg-Maxquardt method for systems of nonlinear equations, and the global convergence result is given. If ｜｜F（x）｜｜ provides a local error bound f which is weaker than the condition of non-singularity for the systems of nonlinear equations, the sequence generated by this modified Levenberg-Marquardt method converges to a point of the solutions set quadratically. Numerical experiments show the effectiveness of this algorithm.
出处
《数值计算与计算机应用》
CSCD
北大核心
2009年第3期186-194,共9页
Journal on Numerical Methods and Computer Applications
基金
中国石油大学(华东)2008年硕士研究生创新基金资助项目(S2008-25)
