解非线性方程组的一种修正Levenberg-Marquardt算法

On a New Modified L-M Method for Solving Nonlinear Equations

提出了求解非线性方程组的一个修正Levenberg-Marquardt方法,每次迭代步都引入校正步,使新的试探步更靠近Moore-Penrose步.另外,利用信赖域技巧修正L-M参数.在弱于雅可比矩阵非奇异的局部误差界条件下,证明了该算法的全局收敛性和局部二次收敛速度.数值试验表明了算法的有效性.

In the paper,we have proposed a new modified Levenberg-Marquardt method for solving nonlinear equations.At every iteration,not only a LM step but also a modified step are computed which makes the trial step closer to the Moore-Penrose step.On the other hand,the LM parameter is updated by the trust region technique.Under the local error bound condition which is weaker than nonsingularity,we prove global and local convergence of this new method.Numerical results show that this new method performs very well.