The LC-Structure-Preserving Algorithms of Quaternion LDLH Decomposition and Cholesky Decomposition

In this paper, the L C -structure-preserving algorithms of L D L H decomposition and Cholesky decomposition of quaternion Hermitian positive definite matrices based on the semi-tensor product of matrices are studied. We first propose L C -representation by using the semi-tensor product of matries an...

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Bibliographic Details
Published in:Advances in applied Clifford algebras Vol. 33; no. 5; p. 57
Main Authors: Zhang, Mingcui, Li, Ying, Sun, Jianhua, Ding, Wenxv
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.11.2023
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Color imagery
Computational mathematics
Decomposition
Mathematical and Computational Physics
Mathematical Methods in Physics
Matrices (mathematics)
Physics
Physics and Astronomy
Quaternions
Representations
Tensors
Theoretical
Cholesky decomposition
structure-preserving
decomposition
representation
Semi-tensor product of matrices
ISSN:0188-7009, 1661-4909
Online Access:Get full text
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Summary:In this paper, the L C -structure-preserving algorithms of L D L H decomposition and Cholesky decomposition of quaternion Hermitian positive definite matrices based on the semi-tensor product of matrices are studied. We first propose L C -representation by using the semi-tensor product of matries and the structure matrix of the product of the quaternion. Then, L C -structure-preserving algorithms of L D L H decomposition and Cholesky decomposition of quaternion Hermitian positive definite matrices are proposed by using L C -representation, and the advantages of our method are obtained by comparing the operation time and error with the real structure-preserving algorithms in Wei et al. (Quaternion matrix computations. Nova Science Publishers, Hauppauge, 2018). Finally, we apply the L C -structure-preserving algorithm of Cholesky decomposition to strict authentication of color images.
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ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-023-01298-4