三次保形有理插值

Rational cubic interpolation with the shape preserved

构造了含有4个参数的分段三次有理样条函数(分子、分母均为三次多项式),其中2个参数称为形状参数,另外2个称为保形参数;通过调整形状参数可交互式修改曲线形状,适当选取保形参数曲线是保单调的。数值例子显示由该样条函数生成的曲线十分光滑且保持了数据固有的形态,最后给出了此插值函数的误差估计。

A piecewise rational cubic spline function involving four parameters is presented, which is a rational polynomial with a cubic numerator and a cubic denominator. The two of the four parameters are called shape parameters ,the other two shape-preserving parameters. Through adjusting shape parameters, one can design the curve interactively and by giving appropriate values to shape-preserving parameters, one can get a monotonic interpolant. Numerical experiments indicate that the method produces a visually pleasant curve and the curve keeps the inherent features of the given data set. Furthermore, the error analysis of the spline interpolant is also given.