| 非线性参数拟合问题的改进阻尼最小二乘方法和共轭梯度方法 |
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| 引用本文： | 赵凤石,姜民奇.非线性参数拟合问题的改进阻尼最小二乘方法和共轭梯度方法[J].齐齐哈尔大学学报(自然科学版),1992(1). |
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| 作者姓名： | 赵凤石 姜民奇 |
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| 作者单位： | 哈尔滨教育学院
(赵凤石)，哈尔滨工业大学(姜民奇) |
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| 摘 要： | 本文首先给出了一个改进的阻尼最小二乘方法,并把它用于非线性曲线拟合问题。由于A~TA为对称正定的就有理由一开始把法方程组做乔累斯基分解,并使法方程的条件数有所改善,为此目的而引入了一个非负的阻尼因子。 对于共轭梯度方法,由于非线性函数在极小点附近表现为二次函数的特性,所以在非线性拟合问题中引入了共轭关系P_j~TAP_j=0共轭梯度方法的优点是收敛速度较快,当它用于二次函数极小化问题时总是在有限步内收敛。
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| 关 键 词： | 阻尼最小二乘方法 共轭梯度方法 非线性参数拟合问题 非线性最优化 非线性规划 |
improving Mothod of Damped Least Square And Method of Conjugate Gradient for Fit Prblems of Nonlinear Parameter |
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| Zhao Fengshi.improving Mothod of Damped Least Square And Method of Conjugate Gradient for Fit Prblems of Nonlinear Parameter[J].Journal of Qiqihar University(Natural Science Edition),1992(1). |
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| Authors: | Zhao Fengshi |
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| Institution: | Zhao Fengshi
(Harbin Eduacational College) Jiang Minqi
(Harbin l nlustrial U n i v e r s i t y ) |
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| Abstract: | This paper first shows you a method which will improve damped least square and then provide it for the problems of the nonlinear curve fit. Since ATA is positive definite symmetric, then it is very reasonable that at the very begining the normal equation set can be decomposed by Choliski skill, and also the condition number improved. For this purpose a nonnegative damping factor is introduced.
Because nonlinear function near minimal point shows the characteristic of square function, the conjugate relation of PjTAPj= 0 is introduced to the nonlinear fit problems the merit of the method of conjugate gradient is the quickness of convergence rate, and when it is used inminimization problems of square function, it converges in definite procedure. |
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| Keywords: | Damped least square method Method of conjugate gradient Fit problems of nonlinear parameter Nonlinear optimization |
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