Error Analysis of the Derivative of the Rational Interpolation Based on Function Values

This paper deals with the approximation properties of the derivatives of rational cubic interpolation based on function values in the field of computer aided geometric design. Error expressions of the derivatives of interpolating functions are derived, convergence is established, and the optimal error coefficient ci is bounded. On the second derivatives, the unified integral form of the error of the second derivatives is obtained in all subintervals except the last subinterval. A simple expression of the jump of the second derivatives at the knots and the conditions of the interpolation function to be C2 in the interpolation interval are given.