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

Javad Golzarpoor, Dilan Ahmed and Stanford Shateyi
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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
Stanford Shateyi: Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Mathematics, 2022, vol. 10, issue 13, 1-11

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.

Keywords: iterative method; matrix square root; higher order; convergence analysis; matrix functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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