eprintid: 7842
rev_number: 2
eprint_status: archive
userid: 1
dir: disk0/00/00/78/42
datestamp: 2023-11-09 16:19:41
lastmod: 2023-11-09 16:19:41
status_changed: 2023-11-09 16:10:33
type: article
metadata_visibility: show
creators_name: Abdul Karim, S.A.
creators_name: Voon Pang, K.
title: Shape preserving interpolation using C2 rational cubic spline
ispublished: pub
keywords: Condition; Cubic-spline interpolation; Free parameters; Interpolants; Knot insertion; Positive data; Rational cubic spline; Shape-preserving interpolation; Tridiagonal systems; Two parameter, Interpolation
note: cited By 10
abstract: This aper discusses the construction of new C 2 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 parametersi, β i, and γ i. The sufficient conditions for the positivity are derived on one parameter γ i while the other two parameters and β i 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 C 2 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 C 2 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 C 2 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 C3 is also investigated in detail. © 2016 Samsul Ariffin Abdul Karim and Kong Voon Pang.
date: 2016
publisher: Hindawi Limited
official_url: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84981229338&doi=10.1155%2f2016%2f4875358&partnerID=40&md5=816b4280eae1a6788d11a3ca5910cfbf
id_number: 10.1155/2016/4875358
full_text_status: none
publication: Journal of Applied Mathematics
volume: 2016
refereed: TRUE
issn: 1110757X
citation:   Abdul Karim, S.A. and Voon Pang, K.  (2016) Shape preserving interpolation using C2 rational cubic spline.  Journal of Applied Mathematics, 2016.   ISSN 1110757X