IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2015y2015i1n572768.html

Positivity Preserving Interpolation Using Rational Bicubic Spline

Author

Listed:
  • Samsul Ariffin Abdul Karim
  • Kong Voon Pang
  • Azizan Saaban

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.

Suggested Citation

  • Samsul Ariffin Abdul Karim & Kong Voon Pang & Azizan Saaban, 2015. "Positivity Preserving Interpolation Using Rational Bicubic Spline," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnljam:v:2015:y:2015:i:1:n:572768
    DOI: 10.1155/2015/572768
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2015/572768
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2015/572768?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Farheen Ibraheem & Maria Hussain & Malik Zawwar Hussain & Akhlaq Ahmad Bhatti, 2012. "Positive Data Visualization Using Trigonometric Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Xinru Liu & Yuanpeng Zhu & Shengjun Liu, 2014. "Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Xingxuan Peng & Zhihong Li & Qian Sun, 2012. "Nonnegativity Preserving Interpolation by ð ¶ 1 Bivariate Rational Spline Surface," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, April.
    4. Xinru Liu & Yuanpeng Zhu & Shengjun Liu, 2014. "Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, May.
    5. Xingxuan Peng & Zhihong Li & Qian Sun, 2012. "Nonnegativity Preserving Interpolation by C1 Bivariate Rational Spline Surface," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Farheen Ibraheem & Maria Hussain & Malik Zawwar Hussain & Akhlaq Ahmad Bhatti, 2012. "Positive Data Visualization Using Trigonometric Function," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xinru Liu & Yuanpeng Zhu & Shengjun Liu, 2014. "Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Xuli Han & Yuanpeng Zhu, 2014. "Total Positivity of the Cubic Trigonometric Bézier Basis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Jin Xie & Xiaoyan Liu, 2014. "The EH Interpolation Spline and Its Approximation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Uzma Bashir & Jamaludin Md. Ali, 2013. "Data Visualization Using Rational Trigonometric Spline," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Samsul Ariffin Abdul Karim & Kong Voon Pang, 2016. "Shape Preserving Interpolation Using C2 Rational Cubic Spline," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).
    6. Yuanpeng Zhu & Xuli Han & Shengjun Liu, 2014. "Quartic Rational Said‐Ball‐Like Basis with Tension Shape Parameters and Its Application," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    7. Tyada, K.R. & Chand, A.K.B. & Sajid, M., 2021. "Shape preserving rational cubic trigonometric fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 866-891.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljam:v:2015:y:2015:i:1:n:572768. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.