On QSOR-Like Iteration Method for Quaternion Saddle Point Problems

With the continuous expansion of the application range of quaternion, the large quaternion saddle point problem appears in the related engineering and technical field, and it is necessary to explore its effective solution. In this paper, for the
$2\times 2$
block quaternion saddle point system, the QSOR-like iterative scheme with parameter matrix is constructed by referring to the traditional SOR iterative method, and the parameter selection of iterative convergence and the selection of preprocessing matrix are analyzed by using the eigenvalue theory of quaternion matrix. Then the complex representation method of quaternion matrix is used to solve the system in Matlab environment. The numerical results show that the established iteration achieves ideal convergence effect by selecting appropriate parameters and preconditioned matrix.