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Some Matrix Iterations for Computing Matrix Sign Function

Author

Listed:
  • F. Soleymani
  • E. Tohidi
  • S. Shateyi
  • F. Khaksar Haghani

Abstract

Some iterative methods are introduced and demonstrated for finding the matrix sign function. It is analytically shown that the new schemes are asymptotically stable. Convergence analysis along with the error bounds of the main proposed method is established. Different numerical experiments are employed to compare the behavior of the new schemes with the existing matrix iterations of the same type.

Suggested Citation

  • F. Soleymani & E. Tohidi & S. Shateyi & F. Khaksar Haghani, 2014. "Some Matrix Iterations for Computing Matrix Sign Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:425654
    DOI: 10.1155/2014/425654
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    References listed on IDEAS

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    1. Michael Trott, 2006. "The Mathematica GuideBook for Numerics," Springer Books, Springer, number 978-0-387-28814-7, March.
    2. Spiros Chountasis & Vasilios N. Katsikis & Dimitrios Pappas, 2009. "Applications of the Moore-Penrose Inverse in Digital Image Restoration," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-12, November.
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    Cited by:

    1. F. Soleymani & M. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. F. Soleymani & P. S. Stanimirović & S. Shateyi & F. Khaksar Haghani, 2014. "Approximating the Matrix Sign Function Using a Novel Iterative Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. F. Soleymani & S. Shateyi & F. Khaksar Haghani, 2014. "A Numerical Method for Computing the Principal Square Root of a Matrix," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. T. Lotfi & F. Soleymani & S. Shateyi & P. Assari & F. Khaksar Haghani, 2014. "New Mono‐ and Biaccelerator Iterative Methods with Memory for Nonlinear Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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