Abstract
This paper deals with the convexity control and the strain energy control of interpolating curves using a rational cubic spline with linear denominator. The sufficient and necessary conditions for controlling the interpolating curve to be convex or concave are derived. When the function being interpolated is f( t)∈ C (3)[ t 0, t n ], the error estimation of the interpolating function and the boundedness of the optimal error coefficient and its double symmetry with regard to parameters are obtained.
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