Computer Engineering and Applications ›› 2014, Vol. 50 ›› Issue (19): 47-52.

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Parameter method of constructing rational interpolating function

SUN Meilan1, ZHU Gongqin2, XIE Jin1   

  1. 1.Department of Mathematics and Physics, Hefei University, Hefei 230601, China
    2.School of Computer and Information, Hefei University of Technology, Hefei 230009, China
  • Online:2014-10-01 Published:2014-09-29


孙梅兰1,朱功勤2,谢  进1   

  1. 1.合肥学院 数学与物理系,合肥 230601
    2.合肥工业大学 计算机与信息学院,合肥 230009

Abstract: 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.

Key words: rational interpolation, parameter, degree type

摘要: 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。

关键词: 有理插值, 参数, 次数类型