CAJ | 학술논문

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=01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。
대설정유리분식함수차수류형적유리삽치문제연구，이유허다흔다적결론。유리삽치문제시부유해，취결우피삽함수일사급정적함수치 f (xi)i=01m+n。지출분자화분모다항식차수지화위N 적유리삽치문제총유해，연후종설정적유리삽치함수차수류형출발，인입정정삼수d，급출일충구조유리삽치함수적방법。용해방법총가이구조출만족삽치조건적유리분식함수，차유교대령활성，계산량야불대。
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=01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.