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Journal of Applied Mathematics
Volume 2014, Article ID 425654, 9 pages
http://dx.doi.org/10.1155/2014/425654
Research Article

Some Matrix Iterations for Computing Matrix Sign Function

1Department of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, Iran
2Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 19 December 2013; Revised 29 May 2014; Accepted 2 June 2014; Published 9 July 2014

Academic Editor: Changbum Chun

Copyright © 2014 F. Soleymani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • F. Soleymani, P. S. Stanimirović, S. Shateyi, and F. Khaksar Haghani, “Approximating the Matrix Sign Function Using a Novel Iterative Method,” Abstract and Applied Analysis, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • F. Soleymani, S. Shateyi, and F. Khaksar Haghani, “A Numerical Method for Computing the Principal Square Root of a Matrix,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Fazlollah Soleymani, Mahdi Sharifi, Solat Karimi Vanani, Farhad Khaksar Haghani, and Adem Kılıçman, “An Inversion-Free Method for Finding Positive Definite Solution of a Rational Matrix Equation,” The Scientific World Journal, vol. 2014, pp. 1–5, 2014. View at Publisher · View at Google Scholar
  • T. Lotfi, F. Soleymani, S. Shateyi, P. Assari, and F. Khaksar Haghani, “New Mono- and Biaccelerator Iterative Methods with Memory for Nonlinear Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • T. Lotfi, F. Soleymani, Z. Noori, A. Kılıçman, and F. Khaksar Haghani, “Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices,” Discrete Dynamics in Nature and Society, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • F. Soleymani, M. Sharifi, S. Shateyi, and F. Khaksar Haghani, “An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign,” Abstract and Applied Analysis, vol. 2014, pp. 1–6, 2014. View at Publisher · View at Google Scholar
  • Eman S. Alaidarous, and Malik Zaka Ullah, “Construction of a convergent scheme for finding matrix sign function,” Applied Mathematics And Computation, vol. 260, pp. 242–248, 2015. View at Publisher · View at Google Scholar
  • F. Khaksar Haghani, “A generalized Steffensen’s method for matrix sign function,” Applied Mathematics and Computation, vol. 260, pp. 249–256, 2015. View at Publisher · View at Google Scholar
  • M. Sharifi, S. Karimi Vanani, F. Khaksar Haghani, M. Arab, and S. Shateyi, “On a Cubically Convergent Iterative Method for Matrix Sign,” The Scientific World Journal, vol. 2015, pp. 1–6, 2015. View at Publisher · View at Google Scholar
  • Haifa Bin Jebreen, “Constructing a High-Order Globally Convergent Iterative Method for Calculating the Matrix Sign Function,” Mathematical Problems in Engineering, vol. 2018, pp. 1–9, 2018. View at Publisher · View at Google Scholar