Shape preserving interpolation using \(C^2\) rational cubic spline
type: Item
instance of: scholarly article
title: Shape preserving interpolation using \(C^2\) rational cubic spline
zbMATH Open document ID: 1435.65025
DOI: 10.1155/2016/4875358
author: Samsul Ariffin Abdul Karim
author: Kong Voon Pang
published in: Journal of Applied Mathematics
publication date: 2019-03-18T00:00:00Z
review text: Summary: This paper 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 parameters \(\alpha_i\), \(\beta_i\), and \(\gamma_i\). The sufficient conditions for the positivity are derived on one parameter \(\gamma_i\) while the other two parameters \(\alpha_i\) and \(\beta_i\) 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 \(d_i\), \(i=1,\dots,n-1\). 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 \(f(t)\in C^3[t_0,t_n]\) is also investigated in detail.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 7037279
Wikidata QID: Q59125198
describes a project that uses: pchip
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/4875358
OpenAlex ID: W2189478049
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description: scientific article; zbMATH DE number 7037279