几种Hermite插值多项式存在唯一性的另一种368-04证明方法及推广的基函数构造方法

Another method for existence and uniqueness with some of Hermite interpolation polynomials and their base function formation

通过计算行列式的值,对几种Hermite插值多项式的存在唯一性给出另一种证明方法,对带不完全导数的m(m≥4)次Hermite插值多项式,给出推广的基函数构造方法,并对带不完全导数的三次及四次Hermite插值多项式的具体实例,给出了基函数的具体表达形式。

By computing the value of the determinant,we give another method to prove existence and uniqueness of Hermite interpolation polynomials,and extend the method for constructing base functions of those m-th（m≥4） degree polynomials with incomplete derivatives. Finally,we obtain the analytic expressions for some base functions of cubic and quartic interpolation,and give an example.