多项式拟合中正规方程组的病态分析和改善

讨论了最小二乘多项式拟合中引起正规方程组病态的两个重要原因:节点对原点的偏离程度和节点坐标的数量级。分析了它们的影响,并提出了改善的办法—数据预处理。 通过这种预处理,可大大降低正规方程组的谱条件数,从而使拟合结果的可靠性得到保证。

Analysis and Improvement on the Ill-Condition of the Normal Equations in the Fitting of a Polynomial

In this paper two reasons-the deviation of the data from the origin and the size of the data-causing the ill-conditioned normal equations in the least square fitting of a polynomial are discussed. And a method to improve the ill-condition is put forward. The method is the data processing in advance. By the means of the data processing in advance the spectral conditional number can be reduced greatly,then the result of the fitting is reliable.