Abstract: The interpolating nodes are sliced and Hermite interpolating polynomial is constructed respectively in this paper. Algebra polynomials which coefficient of the highest order terms is unit are constructed with the remaining nodes. The rational function expression satisfying interpolating conditions is obtained with linear combination method. By introducing parameters, it proves that the osculatory rational interpolation function is existent and unique. And the error estimation formula is produced. Examples show that the proposed mothod is intuitive, flexible, efficient and easy to facilitate to practical application with smaller volume of the calculation.

摘要： 将插值节点进行分段，利用分段Hermite插值多项式及相应的多项式，采用线性组合方法得到一般切触有理插值函数的表达式，还可方便地给出无极点的切触有理插值函数的构造方法。通过引入参数方法，给出设定次数类型的切触有理插值问题有解的条件，证明了解的存在唯一性，并给出误差估计公式。实例表明所给方法具有直观、灵活和有效性，便于实际应用。