Shape Preserving Interpolation Using C 2 Rational Cubic Spline
Joint Authors
Voon Pang, Kong
Abdul Karim, Samsul Ariffin
Source
Journal of Applied Mathematics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-07-19
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
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 α i , β i , and γ i .
The sufficient conditions for the positivity are derived on one parameter γ i while the other two parameters α i 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 d i , 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 f t ∈ C 3 t 0 , t n is also investigated in detail.
American Psychological Association (APA)
Abdul Karim, Samsul Ariffin& Voon Pang, Kong. 2016. Shape Preserving Interpolation Using C 2 Rational Cubic Spline. Journal of Applied Mathematics،Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1107205
Modern Language Association (MLA)
Abdul Karim, Samsul Ariffin& Voon Pang, Kong. Shape Preserving Interpolation Using C 2 Rational Cubic Spline. Journal of Applied Mathematics No. 2016 (2016), pp.1-14.
https://search.emarefa.net/detail/BIM-1107205
American Medical Association (AMA)
Abdul Karim, Samsul Ariffin& Voon Pang, Kong. Shape Preserving Interpolation Using C 2 Rational Cubic Spline. Journal of Applied Mathematics. 2016. Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1107205
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1107205