A new weighted rational cubic interpolation and its approximation

A weighted rational cubic spline interpolation has been constructed using two kinds of rational cubic spline with quadratic denominator. The degree of smoothness of this spline is C2 in the interpolating interval when the parameters satisfy a continuous system. The sufficient and necessary conditions that constrain the interpolant curves to be convex in the interpolating interval or subinterval are derived. Also, the error estimate formulas of this interpolation are obtained.