由等距基点直接构造插值多项式的一种新算法

 现有插值方法,一般都不把插值函数直接表示为代数多项式。本文将提出一种求取插值多项式的分次算法（split-degree argorithm）,可由插值多项式的高次项到其相邻的低次项,通过十分简单的运算,每次算出两个项的系数。本算法的使用限制是插值基点必须等间距。由于本法使用的是相邻差商或差分,故计算工作量小,计算速度快,且可手算。本文算法非常独特,它既不是拉格朗日法,也不是牛顿法。

A NEW ALGORITHM ALLOWING DIRECT CONSTRUCTION OF POLYNOMIAL INTERPOLATING FUNCTIONS WITH EQUALLY-SPACED DATA POINTS

Interpolation methods so far available do not give the interpolating functions directly in the form of algebraic polynomials. The split-degree method of interpolation which the present paper has put forward gives a unique algorithm. With this method the construction of interpolating algebraic polynomials can be carried out by obtaining simultaneously two coefficients of a higher-degree term and its adjacent lower-degree term at a time and in a very simple way. The new algorithm involves only the calculation of adjacent quotient-differences or simply, adjacent differences, thus minimizing the calculation and allowing a fast computing speed. The method is neither Lagrange nor Newton method. A limitation of its application is the requirement of equally-spaced data points.