| 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。 |
| 关键词: 非线性最小二乘,Gauss-Newton法,条件预优共轭梯度法 |
| DOI： |
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| 基金项目:国家自然科学基金 |
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| Exactly Quadratic Convergence and Efficient Implementation of Gauss-Newton Method |
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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. |
| Key words: nonlinear least squares,Guass-Newton method,preconditioned conjugate gradient, |
