IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n318165.html

Two Optimal Eighth‐Order Derivative‐Free Classes of Iterative Methods

Author

Listed:
  • F. Soleymani
  • S. Shateyi

Abstract

Optimization problems defined by (objective) functions for which derivatives are unavailable or available at an expensive cost are emerging in computational science. Due to this, the main aim of this paper is to attain as high as possible of local convergence order by using fixed number of (functional) evaluations to find efficient solvers for one‐variable nonlinear equations, while the procedure to achieve this goal is totally free from derivative. To this end, we consider the fourth‐order uniparametric family of Kung and Traub to suggest and demonstrate two classes of three‐step derivative‐free methods using only four pieces of information per full iteration to reach the optimal order eight and the optimal efficiency index 1.682. Moreover, a large number of numerical tests are considered to confirm the applicability and efficiency of the produced methods from the new classes.

Suggested Citation

  • F. Soleymani & S. Shateyi, 2012. "Two Optimal Eighth‐Order Derivative‐Free Classes of Iterative Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:318165
    DOI: 10.1155/2012/318165
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/318165
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/318165?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. Michael Trott, 2006. "The Mathematica GuideBook for Numerics," Springer Books, Springer, number 978-0-387-28814-7, October.
    2. Alicia Cordero & José L. Hueso & Eulalia Martínez & Juan R. Torregrosa, 2012. "A Family of Derivative‐Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Alicia Cordero & José L. Hueso & Eulalia Martínez & Juan R. Torregrosa, 2012. "A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Mohammed Barrada & Mariya Ouaissa & Yassine Rhazali & Mariyam Ouaissa, 2020. "A New Class of Halley’s Method with Third‐Order Convergence for Solving Nonlinear Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).

    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. Alicia Cordero & Fazlollah Soleymani & Juan R. Torregrosa & Stanford Shateyi, 2014. "Basins of Attraction for Various Steffensen‐Type Methods," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. H. Montazeri & F. Soleymani & S. Shateyi & S. S. Motsa, 2012. "On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. F. Soleymani & M. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "A Class of Steffensen‐Type Iterative Methods for Nonlinear Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. A. S. Al-Fhaid & S. Shateyi & M. Zaka Ullah & F. Soleymani, 2014. "A Matrix Iteration for Finding Drazin Inverse with Ninth‐Order Convergence," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. F. Soleymani & E. Tohidi & S. Shateyi & F. Khaksar Haghani, 2014. "Some Matrix Iterations for Computing Matrix Sign Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    6. F. Soleymani & P. S. Stanimirović & S. Shateyi & F. Khaksar Haghani, 2014. "Approximating the Matrix Sign Function Using a Novel Iterative Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    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:jnlaaa:v:2012:y:2012:i:1:n:318165. 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/4058 .

    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.