Dual quaternion QR decompositon and its corresponding complex structure-preserving algorithms

The dual quaternion matrix has important application value in brain science and multi-agent formation control. In this paper, a practical method for realizing dual quaternion QR decomposition (DQQRD) is proposed by using a dual quaternion Householder transformation. Since the product of dual quatern...

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Bibliographic Details
Published in:Numerical algorithms Vol. 100; no. 3; pp. 1315 - 1331
Main Authors: Sun, Jianhua, Li, Ying, Liu, Xiaochen, Zhang, Mingcui
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2025
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Decomposition
Eigenvalues
Householder transformations
Linear equations
Multiagent systems
Numeric Computing
Numerical Analysis
Quaternions
Tensors
Theory of Computation
Column pivoting
Complex structure-preserving algorithm
The semi-tensor product of matrices
Dual quaternion QR decomposition
Householder transformation
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:The dual quaternion matrix has important application value in brain science and multi-agent formation control. In this paper, a practical method for realizing dual quaternion QR decomposition (DQQRD) is proposed by using a dual quaternion Householder transformation. Since the product of dual quaternions depends on the product law of quaternions, it will face complex computational problems. If DQQRD is directly performed, it will be inefficient. Therefore, in this paper, the complex representation of a dual quaternion matrix is established by using the semi-tensor product (STP) of matrices, and the complex structure-preserving algorithm of the DQQRD is proposed. In order to improve the accuracy of the decomposition, a method of column pivoting is given. Numerical experiments show that the method is effective. Finally, the DQQRD is applied to solve the dual quaternion linear equation A x = b .
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01989-4