Padé型样条的构造

Construction of the Padé-type spline

从Padé样条和Padé型逼近的相关理论出发,利用被插函数在插值点处的函数值以及直到k阶的导数值作为插值条件,构造了Padé型样条,证明了其惟一性,给出其构造方法、数值实例并作出图形。该文构造的Padé型样条不仅可根据被插值函数的特征来选取分母,使其产生较好的逼近效果,而且可避免求解高次非线性方程组,说明了Padé型样条比Padé样条更好地逼近被插值的函数。

Based on the theories of the Padé spline and Padé-type approximation, the Padé-type spline is constructed using both function values and up to k order derivative values of the function being inter- polated as the interpolation da＇ta. Its uniqueness is provedits construction method described and a numerical example presented. The Padé-type spline can not only select denominators by the speciality of the interpolated function to achieve good approximation effect but also avoid solving higher non-linear equations.