逼近离散序列的多项式拟合模型的方法分析研究

Analysis and Research on the Method of Polynomial Fitting Model for Approximating Discrete Sequences

为剖析一般多项式最小二乘法与正交多项式最小二乘法在离散数据拟合模型的差异,利用Matlab对某种食品每件平均单价y与批量x的离散数据建立多项式拟合模型.以拟合误差结果平方和为指标,比较不同拟合次数下一般多项式最小二乘法模型与正交多项式最小二乘法模型的拟合差异.结果表明,随着拟合次数的增加拟合结果的误差更低,拟合结果更精确.当拟合次数相同时,正交多项式最小二乘法比多项式最小二乘法具有更低的误差平方和,获得效果更好的拟合结果.

In order to analyze the difference between the general polynomial least squares method and the orthogonal polynomial least squares method in the discrete data fitting model, a polynomial fitting model was established for the discrete data of the average unit pricey and batch x of a certain food by using Matlab.Taking the square sum of fitting error results as the index, the fitting differences between the general polynomial least squares model and the orthogonal polynomial least squares model under different fitting degrees were compared.The results show that the error of fitting results was lower and the fitting results were more accurate with the increase of fitting times.When the fitting degree was the same, the orthogonal polynomial least squares method has lower error square sum than the polynomial least squares method, and better fitting results were obtained.