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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Vydáno v:Numerical algorithms Ročník 97; číslo 3; s. 1367 - 1382
Hlavní autoři: Wang, Tao, Li, Ying, Wei, Musheng, Xi, Yimeng, Zhang, Mingcui
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.11.2024
Springer Nature B.V
Témata:
Algebra
Algorithms
Computer Science
Coordinate transformations
Decomposition
Numbers
Numeric Computing
Numerical Analysis
Original Paper
Quaternions
Robots
Theory of Computation
Transformations (mathematics)
Gaussian transformation
15B33
Dual quaternion matrix
LU decomposition
Real structure-preserving algorithm
ISSN:1017-1398, 1572-9265
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01753-8