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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, Hindawi, vol. 2014, pages 1-6, August.
    • Handle: RePEc:hin:jnlaaa:978629
    DOI: 10.1155/2014/978629
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    Cited by:

    1. Tao Liu & Ting Li & Malik Zaka Ullah & Abdullah Khamis Alzahrani & Stanford Shateyi, 2024. "An Efficient Iterative Approach for Hermitian Matrices Having a Fourth-Order Convergence Rate to Find the Geometric Mean," Mathematics, MDPI, vol. 12(11), pages 1-12, June.
    2. Urooj Saeed & Sajid Rashid Ahmad & Ghulam Mohey-ud-din & Hira Jannat Butt & Uzma Ashraf, 2022. "An Integrated Approach for Developing an Urban Livability Composite Index—A Cities’ Ranking Road Map to Achieve Urban Sustainability," Sustainability, MDPI, vol. 14(14), pages 1-20, July.
    3. Malik Zaka Ullah, 2021. "A New Inversion-Free Iterative Scheme to Compute Maximal and Minimal Solutions of a Nonlinear Matrix Equation," Mathematics, MDPI, vol. 9(23), pages 1-7, November.

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