IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i6p977-d371902.html
   My bibliography  Save this article

An Efficient Three-Term Iterative Method for Estimating Linear Approximation Models in Regression Analysis

Author

Listed:
  • Siti Farhana Husin

    (Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Terengganu 21300, Malaysia)

  • Mustafa Mamat

    (Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Terengganu 21300, Malaysia)

  • Mohd Asrul Hery Ibrahim

    (Faculty of Entrepreneurship and Business, Universiti Malaysia Kelantan, Kelantan 16100, Malaysia)

  • Mohd Rivaie

    (Department of Computer Sciences and Mathematics, Universiti Teknologi Mara, Terengganu 54000, Malaysia)

Abstract

This study employs exact line search iterative algorithms for solving large scale unconstrained optimization problems in which the direction is a three-term modification of iterative method with two different scaled parameters. The objective of this research is to identify the effectiveness of the new directions both theoretically and numerically. Sufficient descent property and global convergence analysis of the suggested methods are established. For numerical experiment purposes, the methods are compared with the previous well-known three-term iterative method and each method is evaluated over the same set of test problems with different initial points. Numerical results show that the performances of the proposed three-term methods are more efficient and superior to the existing method. These methods could also produce an approximate linear regression equation to solve the regression model. The findings of this study can help better understanding of the applicability of numerical algorithms that can be used in estimating the regression model.

Suggested Citation

  • Siti Farhana Husin & Mustafa Mamat & Mohd Asrul Hery Ibrahim & Mohd Rivaie, 2020. "An Efficient Three-Term Iterative Method for Estimating Linear Approximation Models in Regression Analysis," Mathematics, MDPI, vol. 8(6), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:977-:d:371902
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/6/977/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/6/977/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jinkui Liu & Youyi Jiang, 2012. "Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, July.
    2. Weiyi Qian & Haijuan Cui, 2014. "A New Method with Sufficient Descent Property for Unconstrained Optimization," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, February.
    3. Chia-Nan Wang & Tien-Muoi Le & Han-Khanh Nguyen, 2019. "Application of Optimization to Select Contractors to Develop Strategies and Policies for the Development of Transport Infrastructure," Mathematics, MDPI, vol. 7(1), pages 1-19, January.
    4. Yan Pei & Jun Yu & Hideyuki Takagi, 2019. "Search Acceleration of Evolutionary Multi-Objective Optimization Using an Estimated Convergence Point," Mathematics, MDPI, vol. 7(2), pages 1-18, January.
    5. Ming-Liang Zhang & Yun-Hai Xiao & Dangzhen Zhou, 2010. "A Simple Sufficient Descent Method for Unconstrained Optimization," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-9, December.
    6. Rivaie, Mohd & Mamat, Mustafa & Abashar, Abdelrhaman, 2015. "A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1152-1163.
    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. Mrad, Hatem & Fakhari, Seyyed Mojtaba, 2024. "Optimization of unconstrained problems using a developed algorithm of spectral conjugate gradient method calculation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 282-290.
    2. Rabiu Bashir Yunus & Nooraini Zainuddin & Hanita Daud & Ramani Kannan & Samsul Ariffin Abdul Karim & Mahmoud Muhammad Yahaya, 2023. "A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    3. Johan M. Bogoya & Andrés Vargas & Oliver Schütze, 2019. "The Averaged Hausdorff Distances in Multi-Objective Optimization: A Review," Mathematics, MDPI, vol. 7(10), pages 1-35, September.
    4. Ibrahim Mohammed Sulaiman & Aliyu Muhammed Awwal & Maulana Malik & Nuttapol Pakkaranang & Bancha Panyanak, 2022. "A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing," Mathematics, MDPI, vol. 10(16), pages 1-17, August.

    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:gam:jmathe:v:8:y:2020:i:6:p:977-:d:371902. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.