关键词: 数值逼近, 代数插值, 曲线拟合

Abstract:

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.

Key words: numerical approximation, algebraic interpolation, curve fitting