Positivity Preserving Using C2 Rational Quartic Spline Interpolation

This paper discusses the positivity preserving interpolation of C2 rational quartic spline for positive data. The rational quartic spline has three different parameters which are αi, βi and γi. The proposed rational spline can achieve C2 continuity without the need to solve any tridiagonal systems linear of equations, unlike some other splines that needed solving systems linear of the equation. The sufficient condition is derived on one parameter meanwhile the other two parameters are free parameters that can the user interpolate the final shape of the positive interpolating curve. These conditions will guarantee to produce a positive interpolating curve everywhere. Comparison with the existing schemes also is discussed in detail. From the graphical and numerical results, we found that the proposed scheme is better than existing schemes, since it has an extra free parameter to control the positive interpolating curve while maintaining C2 continuity. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.