A Numerical Method for Computing the Principal Square Root of a Matrix
It is shown how the mid-point iterative method with cubical rate of convergence can be applied for finding the principal matrix square root. Using an identity between matrix sign function and matrix square root, we construct a variant of mid-point method which is asymptotically stable in the neighbo...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/525087 |
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| author | F. Soleymani S. Shateyi F. Khaksar Haghani |
| author_facet | F. Soleymani S. Shateyi F. Khaksar Haghani |
| author_sort | F. Soleymani |
| collection | DOAJ |
| description | It is shown how the mid-point iterative method with cubical rate of convergence can be applied for finding the principal matrix square root. Using an identity between matrix sign function and matrix square root, we construct a variant of mid-point method which is asymptotically stable in the neighborhood of the solution. Finally, application of the presented approach is illustrated in solving a matrix differential equation. |
| format | Article |
| id | doaj-art-f8fedfdd49ee4aa8a7b8c17bfd8814fe |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f8fedfdd49ee4aa8a7b8c17bfd8814fe2025-02-03T01:03:26ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/525087525087A Numerical Method for Computing the Principal Square Root of a MatrixF. Soleymani0S. Shateyi1F. Khaksar Haghani2Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, IranDepartment of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South AfricaDepartment of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, IranIt is shown how the mid-point iterative method with cubical rate of convergence can be applied for finding the principal matrix square root. Using an identity between matrix sign function and matrix square root, we construct a variant of mid-point method which is asymptotically stable in the neighborhood of the solution. Finally, application of the presented approach is illustrated in solving a matrix differential equation.http://dx.doi.org/10.1155/2014/525087 |
| spellingShingle | F. Soleymani S. Shateyi F. Khaksar Haghani A Numerical Method for Computing the Principal Square Root of a Matrix Abstract and Applied Analysis |
| title | A Numerical Method for Computing the Principal Square Root of a Matrix |
| title_full | A Numerical Method for Computing the Principal Square Root of a Matrix |
| title_fullStr | A Numerical Method for Computing the Principal Square Root of a Matrix |
| title_full_unstemmed | A Numerical Method for Computing the Principal Square Root of a Matrix |
| title_short | A Numerical Method for Computing the Principal Square Root of a Matrix |
| title_sort | numerical method for computing the principal square root of a matrix |
| url | http://dx.doi.org/10.1155/2014/525087 |
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