几种有理插值函数的逼近性质

摘要

This paper deals with the approximation properties of some rational cubic splines, inculuding the rational cubic spline with quadratic or linear denominator, the rational cubic spline based on function values. From the point of view of the magnitude of the optimal error constant, it is found that the rational cubic spline with linear denominator gives the best approximation to the function being interpolated. The boundedness of the optimal error constant of the rational splines with linear denominator shows the stability of the interpolating function for the parameters.