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2016 Shape Preserving Interpolation Using C2 Rational Cubic Spline
Samsul Ariffin Abdul Karim, Kong Voon Pang
J. Appl. Math. 2016: 1-14 (2016). DOI: 10.1155/2016/4875358


This paper discusses the construction of new C2 rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parameters αi, βi, and γi. The sufficient conditions for the positivity are derived on one parameter γi while the other two parameters αi and βi are free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation with C2 continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion and C2 continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivatives di, i=1,,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the new C2 rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated is ftC3t0,tn is also investigated in detail.


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Samsul Ariffin Abdul Karim. Kong Voon Pang. "Shape Preserving Interpolation Using C2 Rational Cubic Spline." J. Appl. Math. 2016 1 - 14, 2016.


Received: 18 January 2016; Revised: 10 April 2016; Accepted: 21 April 2016; Published: 2016
First available in Project Euclid: 13 August 2016

zbMATH: 07037279
Digital Object Identifier: 10.1155/2016/4875358

Rights: Copyright © 2016 Hindawi


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