Error analysis of the derivative of rational interpolation with a linear denominator

Abstract

This paper deals with the approximation properties of the derivatives of rational cubic interpolation with a linear denominator. Error expressions of the derivatives of interpolating functions are derived, convergence is established and the optimal error coefficient c _i is proved to be symmetric about the parameters of the rational interpolation. The unified integral form of the error of the second derivative in all subintervals is obtained. A simple expression of the jump of the second derivative at the knots and the conditions for the interpolating function to be C ² in the interpolating interval are given.

Keywords:

• Rational spline
• Error analysis
• Approximation
• Error estimation of derivative

Acknowledgements

The support of the National Nature Science Foundation of China, the Education Foundation of China and the Nature Science Foundation of Shandong Province, China, is gratefully acknowledged.