Rational Cubic Spline for Positivity Preserving Interpolation

Samsul Ariffin Abdul Karim
June 2014
Australian Journal of Basic & Applied Sciences;Jun2014, Vol. 8 Issue 9, p493
Academic Journal
Background: A rational cubic spline scheme is developed with cubic spline as numerator and cubic Ball function as denominator. The two parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The positivity-preserving properties of this rational interpolant, to a given data set are shown. The degree of smoothness C1 is attained (first order of parametric continuity). Objective: Preserving the positive data by using new rational cubic spline and produces the positivee interpolating curves. Results: The sufficient condition for the rational cubic interpolant to be positive are derived and from the numerical results the propose rational cubic spline interpolant gives comparable results. Conclusion: The sufficient condition for positivity constraints were restricted on two shape parameters vi and wi to assure the positivity of the data will be preserved completely. The solution to the shape preserving spline is always exists. We conclude that, the developed scheme work well and is comparable to the existing schemes. It also provides good alternative to the existing rational spline for shape preserving interpolation problem.


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