Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm
Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussi...
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| Veröffentlicht in: | Numerical algorithms Jg. 97; H. 3; S. 1367 - 1382 |
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| Sprache: | Englisch |
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| Abstract | Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussian transformation. We also use the total order of dual numbers to obtain the partial pivoting dual quaternion LU decomposition. Based on the real structure-preserving algorithm of quaternion matrix, we propose the real structure-preserving algorithms of LU decomposition and partial pivoting LU decomposition for dual quaternion matrix. Numerical experiments have verified the effectiveness of the new real structure-preserving approaches. |
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| AbstractList | Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussian transformation. We also use the total order of dual numbers to obtain the partial pivoting dual quaternion LU decomposition. Based on the real structure-preserving algorithm of quaternion matrix, we propose the real structure-preserving algorithms of LU decomposition and partial pivoting LU decomposition for dual quaternion matrix. Numerical experiments have verified the effectiveness of the new real structure-preserving approaches. |
| Author | Zhang, Mingcui Li, Ying Xi, Yimeng Wang, Tao Wei, Musheng |
| Author_xml | – sequence: 1 givenname: Tao surname: Wang fullname: Wang, Tao organization: Research Center of Semi-tensor Product of Matrices: Theory and Applications, College of Mathematical Science, Liaocheng University – sequence: 2 givenname: Ying surname: Li fullname: Li, Ying email: liyingld@163.com organization: Research Center of Semi-tensor Product of Matrices: Theory and Applications, College of Mathematical Science, Liaocheng University – sequence: 3 givenname: Musheng surname: Wei fullname: Wei, Musheng organization: College of Mathematics and Science, Shanghai Normal University – sequence: 4 givenname: Yimeng surname: Xi fullname: Xi, Yimeng organization: Research Center of Semi-tensor Product of Matrices: Theory and Applications, College of Mathematical Science, Liaocheng University – sequence: 5 givenname: Mingcui surname: Zhang fullname: Zhang, Mingcui organization: Research Center of Semi-tensor Product of Matrices: Theory and Applications, College of Mathematical Science, Liaocheng University |
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| Cites_doi | 10.1109/JRA.1987.1087138 10.1115/1.1737378 10.1016/0024-3795(95)00543-9 10.1007/s42967-022-00189-y 10.1109/TMM.2014.2317311 10.1016/j.mechmachtheory.2017.01.013 10.1080/01630563.2022.2108835 10.1016/j.automatica.2021.109817 10.1016/j.patcog.2018.12.013 10.4310/CMS.2023.v21.n7.a5 10.1109/TII.2015.2397878 10.1080/01630563.2023.2254090 10.1007/s10092-017-0241-4 10.1007/s11042-021-11409-7 10.1016/0097-8493(94)90033-7 10.1007/s10915-024-02561-x |
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| Title | Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm |
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