构造有理插值函数的一种参数法

对设定有理分式函数次数类型的有理插值问题研究，已有许多很多的结论。有理插值问题是否有解，取决于被插函数一些给定的函数值f(xi),i=0,1,?,m+n]。指出分子和分母多项式次数之和为N]的有理插值问题总有解，然后从设定的有理插值函数次数类型出发，引入正整参数d]，给出一种构造有理插值函数的方法。用该方法总可以构造出满足插值条件的有理分式函数，且有较大灵活性，计算量也不大。

Parameter method of constructing rational interpolating function

There are a lot of excellent conclusions for the study of rational interpolating problem with the rational fractional function decided degree type. Whether rational interpolating problem has a solution or not depends on the given function values f(xi),i=0,1,?,m+n]of the being interpolated function. It is pointed out that the rational interpolating problem always has solutions when the sum of the degree of numerator polynomial and denominator Poly-nomial is “N”. Proceeding from the hypothetical degree type of rational interpolating function, the positive integer parameter “d” is introduced and a method for the determination of rational interpolating functions is presented. The method can construct rational fraction functions satisfying the interpolating conditions and it is more flexible with a small amount of calculation.