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Approximating the Matrix Sign Function Using a Novel Iterative Method

Author

Listed:
  • F. Soleymani
  • P. S. Stanimirović
  • S. Shateyi
  • F. Khaksar Haghani

Abstract

This study presents a matrix iterative method for finding the sign of a square complex matrix. It is shown that the sequence of iterates converges to the sign and has asymptotical stability, provided that the initial matrix is appropriately chosen. Some illustrations are presented to support the theory.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:105301
    DOI: 10.1155/2014/105301
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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. 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).
    3. F. Soleymani & E. Tohidi & S. Shateyi & F. Khaksar Haghani, 2014. "Some Matrix Iterations for Computing Matrix Sign Function," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, July.
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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. Ce Zhang & Bo Zhao & Wenjing Ren & Ruosong Cao & Tao Liu, 2025. "A Sixth-Order Iterative Scheme Through Weighted Rational Approximations for Computing the Matrix Sign Function," Mathematics, MDPI, vol. 13(17), pages 1-15, September.

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