四元数双鞍点问题分层Uzawa迭代方法

THE HIERARCHICAL UZAWA ITERATION METHOD FOR THE QUATERNION DOUBLE SADDLE POINT PROBLEM

伴随四元数在科技领域的广泛应用,本文提出并讨论3×3分块四元数双鞍点问题的迭代解法.采用适当的矩阵划分方法,将双鞍点问题转化为广义单鞍点问题,从而构建出相应的分层含参Q-Uzawa迭代;再运用四元数矩阵的特征值理论,分析了迭代矩阵的谱值半径,并得到迭代收敛的条件,以及参数的选取方法;最后运用四元数矩阵的复表示方法,在Matlab环境下实现该系统的迭代求解,数值算例检验了所给迭代的可行及有效性.

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.