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Title: Rational Cubic Spline for Positivity Preserving Interpolation
Authors: Samsul Ariffin Abdul Karim
DOI:
Aff: Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak Darul Ridzuan, Malaysia
Author Email:
Keywords: Rational Cubic Spline; Cubic Ball; Positivity; Smoothness
URLs: ABSTRACT-HTML  | FULLTEXT-PDF  | 
Abstract: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 1Cis 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 ivand iw 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.: bol