| 一个结合信赖域技术的修正的Levenberg-Marquardt方法 |
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| 引用本文： | 张华仁,李维国. 一个结合信赖域技术的修正的Levenberg-Marquardt方法[J]. 数值计算与计算机应用, 2009, 30(3): 186-194 |
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| 作者姓名： | 张华仁 李维国 |
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| 作者单位： | 中国石油大学数学与计算科学学院,山东,青岛,266555 |
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| 基金项目： | 中国石油大学(华东)2008年硕士研究生创新基金资助项目 |
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| 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。
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| 关 键 词： | 奇异非线性方程组 Levenberg-Marquardt方法 信赖域技术 全局收敛 局部二阶收敛 |
A MODIFIED LEVENBERG-MARQUATDT METHOD WITH TRUST-REGION TECHNIQUES |
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| Zhang Huaren,Li Weiguo. A MODIFIED LEVENBERG-MARQUATDT METHOD WITH TRUST-REGION TECHNIQUES[J]. Journal on Numerical Methods and Computer Applications, 2009, 30(3): 186-194 |
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| Authors: | Zhang Huaren Li Weiguo |
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| Affiliation: | Zhang Huaren Li Weiguo (School of Mathematics and Computational Sciences, China University of Petroleum, Qingdao 266555, Shandong, China) |
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| Abstract: | 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. |
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| Keywords: | singular nonlinear equations Levenberg-Marquardt method Trust-Region techniques global convergence local quadratic convergence |
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