IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v273y2016icp1051-1058.html
   My bibliography  Save this article

Rational cubic clipping with linear complexity for computing roots of polynomials

Author

Listed:
  • Chen, Xiao-diao
  • Ma, Weiyin

Abstract

Many problems in computer aided geometric design and computer graphics can be turned into a root-finding problem of polynomial equations. Among various clipping methods, the ones based on the Bernstein–Bézier form have good numerical stability. One of such clipping methods is the k-clipping method, where k=2,3 and often called a cubic clipping method when k=3. It utilizes O(n2) time to find two polynomials of degree k bounding the given polynomial f(t) of degree n, and achieves a convergence rate of k+1 for a single root. The roots of the bounding polynomials of degree k are then used for bounding the roots of f(t). This paper presents a rational cubic clipping method for finding two bounding cubics within O(n) time, which can achieve a higher convergence rate 5 than that of 4 of the previous cubic clipping method. When the bounding cubics are obtained, the remaining operations are the same as those of previous cubic clipping method. Numerical examples show the efficiency and the convergence rate of the new method.

Suggested Citation

  • Chen, Xiao-diao & Ma, Weiyin, 2016. "Rational cubic clipping with linear complexity for computing roots of polynomials," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1051-1058.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:1051-1058
    DOI: 10.1016/j.amc.2015.10.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315014058
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.10.054?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Shi & Chen, Guang & Wang, Yigang, 2019. "An improved rational cubic clipping method for computing real roots of a polynomial," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 207-213.

    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:eee:apmaco:v:273:y:2016:i:c:p:1051-1058. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.