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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Bibliographic Details
Published in:Numerical algorithms 2024-11, Vol.97 (3), p.1367-1382
Main Authors: Wang, Tao, Li, Ying, Wei, Musheng, Xi, Yimeng, Zhang, Mingcui
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computer Science
Coordinate transformations
Decomposition
Numbers
Numeric Computing
Numerical Analysis
Original Paper
Quaternions
Robots
Theory of Computation
Transformations (mathematics)
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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01753-8