用Chebyshev多项式预测粮食产量的研究——以吉林省粮食产量为例

在介绍最小二乘法的基本原理的基础上,给出一种Chebyshev多项式进行数据拟合方法,利用此方法对1952～2008年吉林省粮食产量进行了数据分析。结果表明,在进行农业经济研究数据分析时,应用Chebyshev多项式线性最小二乘较优;通过建立的吉林省粮食产量的Chebyshev多项式最小二乘法的预测模型,预测出2009～2015年吉林省的粮食产量分别为2 900.4万、2 983.6万、3 068.1万、3154.0万、3 241.2万、3 329.8万、3 419.7万t;2009～2015年吉林省的粮食产量的年均增产率为2.78%,低于2000～2008年7.12%的年均增长率。

Application of Chebyshev Polynomial in Predicting the Grain Yield

On the basis of introducing the fundamental principles of the least square methods,the Chebyshev polynomial data fitting method is given,by using this method,the grain yield of Jilin Province from 1952 to 2008 is analyzed.The results show that when analyzing the research data of agricultural economy,the least square method of the Chebyshev polynomials is a good choice;by establishing the prediction model of the least square method of Chebyshev polynomials,we get the results that the grain yield in Jilin Province from 2009 to 2015 is 2 9.004millon,2 9.836 million,3 0.681 million,3 1.540 million,3 2.412 million,3 3.298million,3 4.197 million ton;the annual average growth rate of grain yield from 2009 to 2015 is 2.78%,lower than the annual growth rate of 7.12% from 2000 to 2008.