最小二乘分段多项式拟合及其计算机程序

本文运用数理统计的原理,阐述了对平面离散数据进行最小二乘分段多项式拟合的数学模型和方法,估计了拟合曲线的误差,并编制了相应的通用FORTPAN计算程序,能对平面离散数据构成的单值函数曲线和多值函数曲线(在自变量x单调变化的转折点,函数连续而不光滑)进行分段多项式拟合,并能通过适当地选择曲线分界节点、各段多项式次数和各分界节点处连续的导数的阶数,满足很多实际问题的需要和所提出的精度要求。

LEAST SQUARE PIECEWISE POLYNOMIAL FITTING AND ITS PROGRAM

By means of the principles of mathematical statistics, this paper describes a mathematical model and a method of discrete data of plane by least square piecewise polynomial fitting; estimates the errors of the fitting curve; and develops a corresponding current FORTRAN program. This can be used to fit both the single valued function curve and the multiple valued function curve ( at the turning points of monotone change of independendent x, the function is not smooth but continuous) formed by discrete data of plane.Also, this can meet the needs of many practical problems and suggested precisions through properly selecting nodal points of demarcation of the curve and the degree of polynomial of every piece as well as the order of continuous derivative at every nodal points of demarcation.