四元数双鞍点问题分层Uzawa迭代方法OACSTPCD

With the wide application of quaternion in the field of science and technology,this paper proposes and discusses the iterative solution of the 3×3 block quaternion double saddle point problem.By using the appropriate matrix partition method,the double saddle point problem is transformed into a generalized single saddle point problem,so as to construct the corresponding hierarchical parametric Q-Uzawa iteration.Then,by using the eigenvalue theory of quaternion matrix,the spectral radius of the iterative matrix is analyzed,and the condition of iterative convergence and the method of parameter selection are obtained.Finally,the complex representation method of quaternion matrix is used to realize the iterative solution of the system in Matlab environment.The numerical example verifies the feasibility and effectiveness of the given iteration.