## Journal of Applied Mathematics

### Positivity Preserving Interpolation Using Rational Bicubic Spline

#### Abstract

This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free parameters. The sufficient conditions for the positivity are derived on every four boundary curves network on the rectangular patch. Numerical comparison with existing schemes also has been done in detail. Based on Root Mean Square Error (RMSE), our partially blended rational bicubic spline is on a par with the established methods.

#### Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 572768, 15 pages.

Dates
First available in Project Euclid: 15 April 2015

https://projecteuclid.org/euclid.jam/1429105052

Digital Object Identifier
doi:10.1155/2015/572768

Mathematical Reviews number (MathSciNet)
MR3332129

#### Citation

Abdul Karim, Samsul Ariffin; Voon Pang, Kong; Saaban, Azizan. Positivity Preserving Interpolation Using Rational Bicubic Spline. J. Appl. Math. 2015 (2015), Article ID 572768, 15 pages. doi:10.1155/2015/572768. https://projecteuclid.org/euclid.jam/1429105052

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