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Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications

Author

Listed:
  • Javad Golzarpoor

    (Department of Science, School of Mathematical Sciences, University of Zabol, Zabol 98613-35856, Iran)

  • Dilan Ahmed

    (Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Sulaimani 46001, Iraq
    Department of Petroleum Engineering, Komar University of Science and Technology, Kurdistan Region, Sulaymaniyah 46013, Iraq)

  • Stanford Shateyi

    (Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa)

Abstract

In this paper, an improvement to the mid-point method is contributed for finding the square root of a matrix as well as its inverse. To this aim, an iteration scheme to find this matrix function is constructed, and its error and stability estimates are provided to show the theoretical rate of convergence. Our higher-order method can compete with the existing iterative methods of a similar nature. This is illustrated in numerical simulations of various sizes.

Suggested Citation

  • Javad Golzarpoor & Dilan Ahmed & Stanford Shateyi, 2022. "Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications," Mathematics, MDPI, vol. 10(13), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2200-:d:846499
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    References listed on IDEAS

    as
    1. F. Soleymani & S. Shateyi & F. Khaksar Haghani, 2014. "A Numerical Method for Computing the Principal Square Root of a Matrix," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, August.
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