Inversion Free Algorithms for Computing the Principal Square Root of a Matrix
New algorithms are presented about the principal square root of an n×n matrix A. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a sp...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/613840 |
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| _version_ | 1832552353075560448 |
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| author | Nicholas Assimakis Maria Adam |
| author_facet | Nicholas Assimakis Maria Adam |
| author_sort | Nicholas Assimakis |
| collection | DOAJ |
| description | New algorithms are presented about the principal square root of an n×n matrix A. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed. |
| format | Article |
| id | doaj-art-4d012031d63d4ec4bf4a3ba8c434245b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4d012031d63d4ec4bf4a3ba8c434245b2025-02-03T05:58:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/613840613840Inversion Free Algorithms for Computing the Principal Square Root of a MatrixNicholas Assimakis0Maria Adam1Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, 35100 Lamia, GreeceDepartment of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou Street, 35100 Lamia, GreeceNew algorithms are presented about the principal square root of an n×n matrix A. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.http://dx.doi.org/10.1155/2014/613840 |
| spellingShingle | Nicholas Assimakis Maria Adam Inversion Free Algorithms for Computing the Principal Square Root of a Matrix International Journal of Mathematics and Mathematical Sciences |
| title | Inversion Free Algorithms for Computing the Principal Square Root of a Matrix |
| title_full | Inversion Free Algorithms for Computing the Principal Square Root of a Matrix |
| title_fullStr | Inversion Free Algorithms for Computing the Principal Square Root of a Matrix |
| title_full_unstemmed | Inversion Free Algorithms for Computing the Principal Square Root of a Matrix |
| title_short | Inversion Free Algorithms for Computing the Principal Square Root of a Matrix |
| title_sort | inversion free algorithms for computing the principal square root of a matrix |
| url | http://dx.doi.org/10.1155/2014/613840 |
| work_keys_str_mv | AT nicholasassimakis inversionfreealgorithmsforcomputingtheprincipalsquarerootofamatrix AT mariaadam inversionfreealgorithmsforcomputingtheprincipalsquarerootofamatrix |