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.
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