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An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign

Author

Listed:
  • F. Soleymani
  • M. Sharifi
  • S. Shateyi
  • F. Khaksar Haghani

Abstract

Using the relation between a principal matrix square root and its inverse with the geometric mean, we present a fast algorithm for computing the geometric mean of two Hermitian positive definite matrices. The algorithm is stable and possesses a high convergence order. Some experiments are included to support the proposed computational algorithm.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:978629
    DOI: 10.1155/2014/978629
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    File URL: https://doi.org/10.1155/2014/978629
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    References listed on IDEAS

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    1. 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).
    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, Hindawi, vol. 2014, pages 1-9, July.
    3. 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).
    4. 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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