The LC-Structure-Preserving Algorithms of Quaternion LDLH Decomposition and Cholesky Decomposition - Zhang, Mingcui; Li, Ying; Sun, Jianhua; Ding, Wenxv (Advances in applied Clifford algebras, 2023)
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.