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A Matrix Iteration for Finding Drazin Inverse with Ninth‐Order Convergence

Author

Listed:
  • A. S. Al-Fhaid
  • S. Shateyi
  • M. Zaka Ullah
  • F. Soleymani

Abstract

The aim of this paper is twofold. First, a matrix iteration for finding approximate inverses of nonsingular square matrices is constructed. Second, how the new method could be applied for computing the Drazin inverse is discussed. It is theoretically proven that the contributed method possesses the convergence rate nine. Numerical studies are brought forward to support the analytical parts.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:137486
    DOI: 10.1155/2014/137486
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    References listed on IDEAS

    as
    1. Michael Trott, 2006. "The Mathematica GuideBook for Numerics," Springer Books, Springer, number 978-0-387-28814-7, March.
    2. Linlin Zhao, 2012. "The Expression of the Drazin Inverse with Rank Constraints," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Juan R. Torregrosa & Ioannis K. Argyros & Changbum Chun & Alicia Cordero & Fazlollah Soleymani, 2013. "Iterative Methods for Nonlinear Equations or Systems and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-2, September.
    4. Juan R. Torregrosa & Ioannis K. Argyros & Changbum Chun & Alicia Cordero & Fazlollah Soleymani, 2013. "Iterative Methods for Nonlinear Equations or Systems and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    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. F. Soleymani, 2012. "A Rapid Numerical Algorithm to Compute Matrix Inversion," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, September.
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