A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications
In this paper, based on the Gauss transformation of a quaternion matrix, we study the full rank decomposition of a quaternion matrix, and obtain a direct algorithm and complex structure-preserving algorithm for full rank decomposition of a quaternion matrix. In addition, we expand the application of...
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| Published in | Numerical algorithms Vol. 91; no. 4; pp. 1461 - 1481 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.12.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1017-1398 1572-9265 |
| DOI | 10.1007/s11075-022-01310-1 |
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| Abstract | In this paper, based on the Gauss transformation of a quaternion matrix, we study the full rank decomposition of a quaternion matrix, and obtain a direct algorithm and complex structure-preserving algorithm for full rank decomposition of a quaternion matrix. In addition, we expand the application of the above two full rank decomposition algorithms and give a fast algorithm to calculate the quaternion linear equations. The numerical examples show that the complex structure-preserving algorithm is more efficient. Finally, we apply the structure-preserving algorithm of the full rank decomposition to the sparse representation classification of color images, and the classification effect is well. |
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| AbstractList | In this paper, based on the Gauss transformation of a quaternion matrix, we study the full rank decomposition of a quaternion matrix, and obtain a direct algorithm and complex structure-preserving algorithm for full rank decomposition of a quaternion matrix. In addition, we expand the application of the above two full rank decomposition algorithms and give a fast algorithm to calculate the quaternion linear equations. The numerical examples show that the complex structure-preserving algorithm is more efficient. Finally, we apply the structure-preserving algorithm of the full rank decomposition to the sparse representation classification of color images, and the classification effect is well. |
| Author | Zhang, Dong Wang, Gang Jiang, Tongsong Vasiliev, Vasily. I. |
| Author_xml | – sequence: 1 givenname: Gang orcidid: 0000-0001-6008-630X surname: Wang fullname: Wang, Gang organization: Institute of Mathematics and Information Science, North-Eastern Federal University, School of Mathematics and Statistics, Heze University – sequence: 2 givenname: Dong surname: Zhang fullname: Zhang, Dong organization: Institute of Mathematics and Information Science, North-Eastern Federal University, School of Mathematics and Statistics, Heze University – sequence: 3 givenname: Vasily. I. surname: Vasiliev fullname: Vasiliev, Vasily. I. email: vasvasil@mail.ru organization: Institute of Mathematics and Information Science, North-Eastern Federal University – sequence: 4 givenname: Tongsong surname: Jiang fullname: Jiang, Tongsong email: jiangtongsong@sina.com organization: Institute of Mathematics and Information Science, North-Eastern Federal University, School of Mathematics and Statistics, Heze University, School of Mathematics and Statistics, Linyi University |
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| Cites_doi | 10.1016/j.cam.2018.06.015 10.1016/0370-2693(94)91265-3 10.1007/BF02759321 10.1023/A:1026626424174 10.1016/j.cpc.2013.05.001 10.1016/j.cam.2012.09.018 10.1016/j.jappgeo.2018.12.017 10.1002/mma.5917 10.1016/j.camwa.2017.10.009 10.1007/s10586-016-0685-3 10.13001/1081-3810.1101 10.1063/1.1794368 10.1007/s10092-017-0241-4 10.1016/j.cam.2016.03.031 10.1007/s00521-014-1582-4 10.1016/j.cpc.2014.11.016 10.1016/0167-8191(88)90070-1 |
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| Keywords | Complex structure-preserving algorithm Full rank decomposition Quaternion matrix Sparse representation classification 15A33 Complex representation |
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| SubjectTerms | Algebra Algorithms Color imagery Computer Science Decomposition Image classification Linear equations Numeric Computing Numerical Analysis Original Paper Quaternions Theory of Computation |
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| Title | A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications |
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