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

In this paper, the L-C-structure-preserving algorithms of LDLH 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 LDLH 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.