A New Complex Structure-Preserving Method for QSVD

In this paper, we propose a new structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix A. We first prove that the multiplication of two complex adjoint matrices will still be a complex adjoint matrix. Thus, utilizing this fact, we conduct a sequence of unitary complex adjoint matrices on a half of the elements of the complex adjoint matrix \(\chi _A\) ${\chi }_A$ of A instead of the whole \(\chi _A\) ${\chi }_A$ . Then, we recover the resulting matrix with the help of the special structures. This method also reveals an efficient way to preserve some specific structures implicitly. Moreover, comparing with other algorithms, the numerical experiments show that our algorithm has higher accuracy when computing the QSVD of a large scale quaternion matrix.