数学杂志2024，Vol.44Issue(3)：236-246,11.
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
摘要
Abstract
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.关键词
四元数/双鞍点问题/分层Uzawa迭代/收敛条件/参数选取Key words
quaternion/double saddle point problem/layered Uzawa iteration/convergence conditions/parameter selection分类
数理科学引用本文复制引用
张燕婷,黄敬频..四元数双鞍点问题分层Uzawa迭代方法[J].数学杂志,2024,44(3):236-246,11.基金项目
国家自然科学基金项目(12361078) （12361078）
广西科技基地和人才专项(桂科-AD23023001). （桂科-AD23023001）
