稀疏近似逆预处理求解一类矩阵方程  

Solving a Class of Matrix Equations by Sparse Approximate Inverse Preconditioning

作　　者：邓淼[1] 周富照[1] 

机构地区：[1]长沙理工大学数学与统计学院,长沙410114

出　　处：《数学理论与应用》2017年第1期38-43,共6页Mathematical Theory and Applications

基　　金：国家自然科学基金资助项目(11371072)

摘　　要：本文给出一类矩阵方程的基于F-范数最小化的稀疏近似逆预处理方法.首先,运用基于F-范数最小化的稀疏近似逆技术寻求一个有效的预处理子M.然后,将得到的预处理子运用到正交投影迭代法中,得到新的算法,并证明算法的收敛性.最后,通过数值实例来验证预处理方法的有效性.In this paper a F-norm minimization based sparse approximate inverse preconditioning for solving a class of matrix equations is given. Firstly, the effective preeonditioner is find by the F--norm minimization based sparse approximate inverse preconditioning technique, then a algorithm is given by applying the obtained preeonditioner in the orthogonal projection iteration method and the convergence of the algorithm is showed. Finally, a numerical example is presented to verify the effectiveness of the algorithm.

关 键 词：矩阵方程 正交投影迭代法 预条件 稀疏近似逆 

分 类 号：O241.6[理学—计算数学]