构造有理插值函数的一种参数法  

Parameter method of constructing rational interpolating function

作　　者：孙梅兰[1] 朱功勤[2] 谢进[1] 

机构地区：[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

出　　处：《计算机工程与应用》2014年第19期47-52,共6页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11026076);教育部科学技术研究重大项目(No.309017);安徽省教育厅自然科研基金(No.KJ2010B182);合肥学院科研重点项目(No.13KY03ZD;No.12KY02ZD)

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。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.

关 键 词：有理插值 参数 次数类型 

分 类 号：O241.5[理学—计算数学]