| Gauss-Newton法恰2阶收敛性及其有效实现 |
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| 引用本文： | 周志坚,王兆智.Gauss-Newton法恰2阶收敛性及其有效实现[J].中国农业大学学报,1999,4(2):31-35. |
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| 作者姓名： | 周志坚 王兆智 |
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| 作者单位： | 中国农业大学工程基础科学部 |
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| 摘 要： | 研究求解零残差非线性最小二乘问题的算法。给出了保证Gauss-Newton法恰2阶收敛的条件，在此基础上构造了利用条件预化共轭梯度法求解Gauss-Newton方程的新的有效算法。新算法与传统的使用Choleski技术的Gauss-Newton法具有相同的收敛速率，但在求解Gauss-Newton方程组时减少了代数运算的计算量。如维数n＝200时，其计算量大体可减少35％，且当n趋于无穷时，两者的计算量之比以In2／Inn的速度趋于零。
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| 关 键 词： | 非线性最小二乘 Gauss-Newton法 条件预优共轭梯度法 |
Exactly Quadratic Convergence and Efficient Implementation of Gauss-Newton Method |
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| Zhuo Zhijian,Wang Zhaozhi.Exactly Quadratic Convergence and Efficient Implementation of Gauss-Newton Method[J].Journal of China Agricultural University,1999,4(2):31-35. |
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| Authors: | Zhuo Zhijian Wang Zhaozhi |
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| Abstract: | The methods to solve the nonlinear least squares problem with zero vesidual arediscussed. A sufficient condition ensuring the Gauss-Newton method quadraticallyconvergent exactly is given. Based on it, a new efficient implementation of preconditionedconjugate gradient is put forward to solve the Gauss-Newton equation and save the cost oncomputation with the same exactly quadratic convergence to the traditional choleskifactorization. The ratio of computation will decrease 35% when n=200 and reduce to zero atthe rate of ln 2/ln n when n is infinite. |
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| Keywords: | nonlinear least squares Guass-Newton method preconditioned conjugate gradient |
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