一类向量值切触有理插值函数的构造

Constructing of a Vector-Valued Osculatory Rational Interpolation Functions

切触有理插值是Hermite插值的一种推广,熟知的构造向量值切触有理插值函数的方法都与连分式有关,算法的可行性不易预知,并且计算量太大.本文通过引入有理基函数和插值算子,定义了一对多项式:代数多项式和向量多项式,从而给出了向量值切触有理插值公式,并将其推广到高阶向量值切触有理插值函数的构造中.此外,若选择适当的参数,可以降低分母的次数.该方法简单,具有可操作性和实际应用价值.数值例子表明了该方法的有效性.

Osculatory rational interpolation is a generalization of Hermite interpolation, the well - known algo- rithms of constructing vector - valued osculatory rational interpolations which are all related to continued frac- tions. Their applicability is not easily forecast and they need a large amount of calculation. In this paper, a group of polynomials, namely, an algebraic polynomial and vector- valued polynomials are defined by the introduction of rational basis function and interpolation operator, and the vector- valued osculatory rational interpolation for- mula is given. It is then generalized to vector - valued osculatory rational interpolants of higher orders. Moreo- ver, if appropriate parameters are selected, it can reduce the number of the denominator. The method is simple, it is apt to be operated and feasible in practice. The examples that the method is effective.