| 一种新的求解非线性最小二乘问题的牛顿迭代算法 |
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| 引用本文： | 唐利民.一种新的求解非线性最小二乘问题的牛顿迭代算法[J].长沙交通学院学报,2008,24(3):18-23. |
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| 作者姓名： | 唐利民 |
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| 作者单位： | 长沙理工大学,交通运输工程学院,湖南,长沙,410076;中南大学,信息物理工程学院,湖南,长沙,410083 |
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| 摘 要： | 通过对普通牛顿迭代法的Hessian矩阵添加一个正则化因子，改善迭代过程中Hessian矩阵的病态程度，构造出一种新的求解不适定非线性最小二乘问题牛顿迭代算法，并给出算法迭代步骤，解决了普通牛顿迭代法在迭代过程中其Hessian矩阵秩亏或者严重病态而导致不能收敛的问题，最后，以地基沉降-时间关系预测的泊松模型为例，进行了数值分析实验，结果表明本研究中所提方法是适用的．
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| 关 键 词： | 不适定 非线性最小二乘 Hessian矩阵 牛顿迭代 泊松模型 |
A new newton iterative algorithm for solving nonlinear least squares problem |
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| TANG Li-min.A new newton iterative algorithm for solving nonlinear least squares problem[J].Journal of Changsha Communications University,2008,24(3):18-23. |
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| Authors: | TANG Li-min |
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| Institution: | TANG Li-min ( School of Traffic and Transportation Engineering, Changsha University of Science ＆ Technology, Changsha 410076 China ; College of Info-Physies and Geomaties Engineering, Central South University, Changsha 410083, China) |
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| Abstract: | A regularization factor added to Hessian matrix in newton iterative method for reducing the Hessian matrix's ill-position in iterative process.A new newton iterative method for ill-posed nonlinear least squares problem was constructed,the iterative steps were proposed for the method,which can solve the problem when the Hessian matrix is rank-deficient or severely ill-posed in iterative process.Numerical experiment showsd that the method which is given is applicabile by testifying the poisson model which is used for predicting the relationship between foundation settlement and time. |
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| Keywords: | ill-posed nonlinear least squares Hessian matrix newton iterative poisson model |
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