水泵性能曲线的正交多项式拟合

Orthogonal Polynomial Fitting for Pump Characteristic Curves

采用不规则点的正交多项式来拟合水泵性能曲线 ,可避免采用一般多项式拟合时可能出现病态方程组的弊端。文中采用 Forsythe递推法生成正交多项式 ,根据显著性检验来确定拟合的多项式次数 ,并在计算中佐以作图程序来进行直观分析。文中还结合具体的算例证明了这种方法的实用性。

Orthogonal polynomial is used to fit the characteristic curves of pump with rand om data to avoid the ill-conditioned system of equations that probably appears i n ordinary polynomial fitting. The Forsythe Recurrence Method is adopted to gene rate the orthogonal polynomial, and the degree of the polynomial is determined b y significance test. Using drawing program to make intuitive analysis for the co mputation, the method is shown to be practical by several actual examples.