高斯-牛顿法及其在作物水分生产函数模型参数求解中的应用  

Application of Gauss-Newton Method in Calculation of Parameters of Crop Water Production Function

作　　者：罗玉峰[1] 崔远来[1] 朱秀珍[1] 

机构地区：[1]武汉大学水利水电学院,湖北武汉430072

出　　处：《节水灌溉》2004年第1期1-2,8,共3页Water Saving Irrigation

基　　金：863计划项目"现代灌溉条件下水肥耦合与高效利用技术(2001AA242032-4)";"南方季节性缺水灌区(江西省鹰潭)节水农业综合技术体系集成与示范(2002AA2Z4331)"部分研究内容。

摘　　要：对于作物水分生产函数的非线性模型,现有参数求解方法是先采用变量代换使模型线性化后再用最小二乘法求解。用这种方法得到的参数估计值并不是无偏估计,因而回归方程也不是最优的,相应相关系数也不能很好地反映拟合的显著性水平。介绍了高斯 牛顿法,并把它用于作物水分生产函数Jensen模型参数求解,该方法可使拟合结果逼近无偏估计,从而提高拟合的精度。同时,给出的未经线性化模型的相关系数更能反映拟合的显著性水平。The present calculation method for parameters of nonlinear model of crop water production function is firstly using variable substitution to convert it into linear model, and then using least square method to calculate it. However, the estimation value of parameter achieved by using this method is not unbiased ,so the regressive function is not optimal and the correlative coefficient can not measure the performance of fitting efficiently. This paper introduces Gauss-Newton method and uses it to calculate the parameters of Jensen model of crop water production function. The result by using this method is nearly unbiased, the fitting precision is enhanced and the correlative coefficient of original model presented can measure the performance of fitting more efficiently.

关 键 词：作物水分生产函数 模型参数 非线性回归 高斯-牛顿法 相关系数 灌溉 

分 类 号：S274.4[农业科学—农业水土工程]