IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v290y2016icp98-110.html
   My bibliography  Save this article

An improved Newton–Traub composition for solving systems of nonlinear equations

Author

Listed:
  • Sharma, Janak Raj
  • Sharma, Rajni
  • Bahl, Ashu

Abstract

In this paper, we present a modified Newton–Traub composition with increasing order of convergence for solving systems of nonlinear equations. The idea is based on the recent development by Sharma et al. (2015). Analysis of convergence shows that the presented method has sixth order of convergence. Computational efficiency of the new method is considered and compared with some well-known existing methods. Numerical tests are performed on some problems of different nature, which confirm robust and efficient convergence behavior of the proposed method. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems. The basins of attraction of existing methods and the presented method are given to demonstrate their performance.

Suggested Citation

  • Sharma, Janak Raj & Sharma, Rajni & Bahl, Ashu, 2016. "An improved Newton–Traub composition for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 98-110.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:98-110
    DOI: 10.1016/j.amc.2016.05.051
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316303691
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.05.051?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.

    References listed on IDEAS

    as
    1. Xiao, Xiaoyong & Yin, Hongwei, 2015. "A new class of methods with higher order of convergence for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 300-309.
    2. Narang, Mona & Bhatia, Saurabh & Kanwar, V., 2016. "New two-parameter Chebyshev–Halley-like family of fourth and sixth-order methods for systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 394-403.
    3. Sharma, Janak Raj & Sharma, Rajni & Kalra, Nitin, 2015. "A novel family of composite Newton–Traub methods for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 520-535.
    4. Rostamy, Davoud & Bakhtiari, Parisa, 2015. "New efficient multipoint iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 350-356.
    5. Esmaeili, H. & Ahmadi, M., 2015. "An efficient three-step method to solve system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1093-1101.
    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. Amiri, Abdolreza & Argyros, Ioannis K., 2021. "On the approximation of mth power divided differences preserving the local order of convergence," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Bahl, Ashu & Cordero, Alicia & Sharma, Rajni & R. Torregrosa, Juan, 2019. "A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 147-166.

    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. Bahl, Ashu & Cordero, Alicia & Sharma, Rajni & R. Torregrosa, Juan, 2019. "A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 147-166.
    2. Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. Abbasbandy, Saeid & Bakhtiari, Parisa & Cordero, Alicia & Torregrosa, Juan R. & Lotfi, Taher, 2016. "New efficient methods for solving nonlinear systems of equations with arbitrary even order," Applied Mathematics and Computation, Elsevier, vol. 287, pages 94-103.
    4. Beny Neta, 2021. "A Note on Traub’s Method for Systems of Nonlinear Equations," Mathematics, MDPI, vol. 9(23), pages 1-8, November.
    5. Hessah Faihan Alqahtani & Ramandeep Behl & Munish Kansal, 2019. "Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    6. Chun, Changbum & Neta, Beny, 2019. "Developing high order methods for the solution of systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 178-190.
    7. Ramandeep Behl & Ioannis K. Argyros, 2020. "A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    8. Marcos Tostado-Véliz & Salah Kamel & Francisco Jurado & Francisco J. Ruiz-Rodriguez, 2021. "On the Applicability of Two Families of Cubic Techniques for Power Flow Analysis," Energies, MDPI, vol. 14(14), pages 1-15, July.
    9. Abro, Hameer Akhtar & Shaikh, Muhammad Mujtaba, 2019. "A new time-efficient and convergent nonlinear solver," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 516-536.
    10. Xiao, Xiao-Yong & Yin, Hong-Wei, 2018. "Accelerating the convergence speed of iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 8-19.
    11. Ramandeep Behl & Ioannis K. Argyros & Sattam Alharbi, 2024. "Accelerating the Speed of Convergence for High-Order Methods to Solve Equations," Mathematics, MDPI, vol. 12(17), pages 1-22, September.
    12. Ramandeep Behl & Ioannis K. Argyros & Sattam Alharbi, 2024. "A One-Parameter Family of Methods with a Higher Order of Convergence for Equations in a Banach Space," Mathematics, MDPI, vol. 12(9), pages 1-18, April.
    13. Janak Raj Sharma & Deepak Kumar & Ioannis K. Argyros & Ángel Alberto Magreñán, 2019. "On a Bi-Parametric Family of Fourth Order Composite Newton–Jarratt Methods for Nonlinear Systems," Mathematics, MDPI, vol. 7(6), pages 1-27, May.
    14. José J. Padilla & Francisco I. Chicharro & Alicia Cordero & Alejandro M. Hernández-Díaz & Juan R. Torregrosa, 2024. "A Class of Efficient Sixth-Order Iterative Methods for Solving the Nonlinear Shear Model of a Reinforced Concrete Beam," Mathematics, MDPI, vol. 12(3), pages 1-16, February.
    15. Ramandeep Behl & Ioannis K. Argyros & Jose Antonio Tenreiro Machado, 2020. "Ball Comparison between Three Sixth Order Methods for Banach Space Valued Operators," Mathematics, MDPI, vol. 8(5), pages 1-12, April.
    16. Narang, Mona & Bhatia, Saurabh & Kanwar, V., 2016. "New two-parameter Chebyshev–Halley-like family of fourth and sixth-order methods for systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 394-403.
    17. Deepak Kumar & Ioannis K. Argyros & Janak Raj Sharma, 2018. "Convergence Ball and Complex Geometry of an Iteration Function of Higher Order," Mathematics, MDPI, vol. 7(1), pages 1-13, December.

    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:290:y:2016:i:c:p:98-110. 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: 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.