The approximation properties of some rational cubic splines

Abstract

This paper deals with the approximation properties of some typical rational cubic splines, including the case with cubic, quadratic or linear denominator. 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.

Keywords:

• Rational spline
• cubic spline
• approximation property
• optimal error constant

C.R. Categories:

• G.1.2