Journal of Applied Mathematics

Shape Preserving Interpolation Using C2 Rational Cubic Spline

Samsul Ariffin Abdul Karim and Kong Voon Pang

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Abstract

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.

Article information

Source
J. Appl. Math., Volume 2016 (2016), Article ID 4875358, 14 pages.

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

Permanent link to this document
https://projecteuclid.org/euclid.jam/1471050610

Digital Object Identifier
doi:10.1155/2016/4875358

Citation

Abdul Karim, Samsul Ariffin; Voon Pang, Kong. Shape Preserving Interpolation Using ${C}^{2}$ Rational Cubic Spline. J. Appl. Math. 2016 (2016), Article ID 4875358, 14 pages. doi:10.1155/2016/4875358. https://projecteuclid.org/euclid.jam/1471050610


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