摘要
作者在研究正交多项式的最小二乘拟合算法时发现当观测数据的趋势是某一个N次多项式时会出现一种现象,即不能找到最佳的最小二乘拟合多项式。为此,作者利用统计学中的零假设及其结论,以方差代替平方误差,然后用多组服从零平均正态分布的随机模拟误差,经程序反复计算,结果表明用方差代替平方误差能克服上述现象,并找出最佳拟合多项式。最后用一个生产实例简要说明了该研究的实际意义。
It is difficult to find the best least square polynomial to fitting the curve of observed data when the graph of fitted data is approximate to N-polynomial. In this thesis, the new fitting method is obtained by using the variance instead of the error of square . This method is based on zero hypothesis and their related results in statistic. After many data test , we find that this new method is better than the classical least square polynomial method in this case . At last , an example is given to illustrate our result.
出处
《贵州大学学报（自然科学版）》
2007年第2期111-115,119,共6页
Journal of Guizhou University:Natural Sciences
基金
贵州大学重点课程建设基金资助项目(贵州省教育厅自然科学基金资助项目(2004201))
关键词
最小二乘法
正交多项式
零假设
零平均正态分布
伪随机数
Least-squates methord
Or thogonal Polynomial
Zero assumption
Zero average normal distribution
Pseudo-random number
