Error estimation of a kind of rational spline

This paper deals with the approximation properties of a kind of rational spline with linear denominator when the function being interpolated is C 3 in an interpolating interval. Error estimate expressions of interpolating functions are derived, convergence is established, the optimal error coefficient, c i , is proved to be symmetric about the parameters of the rational interpolation and it is bounded. Finally, the precise jump measurements of the second derivatives of the interpolating function at the knots are given.