Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications
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 conver...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2200 |
| _version_ | 1797434120585871360 |
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| author | Javad Golzarpoor Dilan Ahmed Stanford Shateyi |
| author_facet | Javad Golzarpoor Dilan Ahmed Stanford Shateyi |
| author_sort | Javad Golzarpoor |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T10:27:42Z |
| format | Article |
| id | doaj.art-ed74b35d90854e258fc7f5190d719342 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:27:42Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ed74b35d90854e258fc7f5190d7193422023-12-01T21:35:02ZengMDPI AGMathematics2227-73902022-06-011013220010.3390/math10132200Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and ApplicationsJavad Golzarpoor0Dilan Ahmed1Stanford Shateyi2Department of Science, School of Mathematical Sciences, University of Zabol, Zabol 98613-35856, IranDepartment of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Sulaimani 46001, IraqDepartment of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South AfricaIn 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.https://www.mdpi.com/2227-7390/10/13/2200iterative methodmatrix square roothigher orderconvergence analysismatrix functions |
| spellingShingle | Javad Golzarpoor Dilan Ahmed Stanford Shateyi Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications Mathematics iterative method matrix square root higher order convergence analysis matrix functions |
| title | Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications |
| title_full | Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications |
| title_fullStr | Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications |
| title_full_unstemmed | Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications |
| title_short | Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications |
| title_sort | constructing a matrix mid point iterative method for matrix square roots and applications |
| topic | iterative method matrix square root higher order convergence analysis matrix functions |
| url | https://www.mdpi.com/2227-7390/10/13/2200 |
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