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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Linlin Zhao, 2012. "The Expression of the Drazin Inverse with Rank Constraints," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, November.
    6. 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.
    7. 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.
    8. 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.
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