IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i7p622-d248023.html
   My bibliography  Save this article

A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

Author

Listed:
  • Dilan Ahmed

    (Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Sulaimani 46001, Iraq)

  • Mudhafar Hama

    (Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Sulaimani 46001, Iraq)

  • Karwan Hama Faraj Jwamer

    (Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Sulaimani 46001, Iraq)

  • Stanford Shateyi

    (Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa)

Abstract

One of the most important generalized inverses is the Drazin inverse, which is defined for square matrices having an index. The objective of this work is to investigate and present a computational tool in the form of an iterative method for computing this task. This scheme reaches the seventh rate of convergence as long as a suitable initial matrix is chosen and by employing only five matrix products per cycle. After some analytical discussions, several tests are provided to show the efficiency of the presented formulation.

Suggested Citation

  • Dilan Ahmed & Mudhafar Hama & Karwan Hama Faraj Jwamer & Stanford Shateyi, 2019. "A Seventh-Order Scheme for Computing the Generalized Drazin Inverse," Mathematics, MDPI, vol. 7(7), pages 1-10, July.
  • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:622-:d:248023
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/7/622/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/7/7/622/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Haifa Bin Jebreen & Yurilev Chalco-Cano, 2018. "An Improved Computationally Efficient Method for Finding the Drazin Inverse," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-8, October.
    2. Linlin Zhao, 2012. "The Expression of the Drazin Inverse with Rank Constraints," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, November.
    3. Ma, Jie & Gao, Feng & Li, Yongshu, 2019. "An efficient method to compute different types of generalized inverses based on linear transformation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 367-380.
    4. Fazlollah Soleymani, 2019. "Efficient Semi-Discretization Techniques for Pricing European and American Basket Options," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1487-1508, April.
    5. Farahnaz Soleimani & Fazlollah Soleymani & Stanford Shateyi, 2013. "Some Iterative Methods Free from Derivatives and Their Basins of Attraction for Nonlinear Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-10, April.
    6. Zhiping Xiong & Zhongshan Liu, 2019. "The Forward Order Law for Least Square g -Inverse of Multiple Matrix Products," Mathematics, MDPI, vol. 7(3), pages 1-10, March.
    7. Xiaoji Liu & Guangyan Zhu & Guangping Zhou & Yaoming Yu, 2012. "An Analog of the Adjugate Matrix for the Outer Inverse ð ´ ( 2 ) 𠑇 , 𠑆," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-14, February.
    8. Predrag S. Stanimirović & Miroslav Ćirić & Igor Stojanović & Dimitrios Gerontitis, 2017. "Conditions for Existence, Representations, and Computation of Matrix Generalized Inverses," Complexity, Hindawi, vol. 2017, pages 1-27, June.
    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. Haifa Bin Jebreen, 2019. "Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration Scheme," Mathematics, MDPI, vol. 7(8), pages 1-11, August.
    2. Kansal, Munish & Kumar, Sanjeev & Kaur, Manpreet, 2022. "An efficient matrix iteration family for finding the generalized outer inverse," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. Stanimirović, Predrag S. & Petković, Marko D. & Mosić, Dijana, 2022. "Exact solutions and convergence of gradient based dynamical systems for computing outer inverses," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    4. Jian Li & Xiaomeng Wang & Kalyanasundaram Madhu, 2019. "Higher-Order Derivative-Free Iterative Methods for Solving Nonlinear Equations and Their Basins of Attraction," Mathematics, MDPI, vol. 7(11), pages 1-15, November.
    5. Stanimirović, Predrag S. & Ćirić, Miroslav & Lastra, Alberto & Sendra, Juan Rafael & Sendra, Juana, 2021. "Representations and symbolic computation of generalized inverses over fields," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    6. Ashim Kumar & Dijana Mosić & Predrag S. Stanimirović & Gurjinder Singh & Lev A. Kazakovtsev, 2022. "Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    7. Dijana Mosić & Predrag S. Stanimirović & Spyridon D. Mourtas, 2023. "Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    8. Stanimirović, Predrag S. & Mosić, Dijana & Wei, Yimin, 2022. "Generalizations of composite inverses with certain image and/or kernel," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    9. Chan, Eunice Y.S. & Corless, Robert M. & González-Vega, Laureano & Sendra, J. Rafael & Sendra, Juana, 2022. "Inner Bohemian inverses," Applied Mathematics and Computation, Elsevier, vol. 421(C).

    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:7:y:2019:i:7:p:622-:d:248023. 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.