稀疏近似逆预处理求解一类矩阵方程

数学理论与应用 ›› 2017, Vol. 37 ›› Issue (1): 38-43.

稀疏近似逆预处理求解一类矩阵方程

邓淼，周富照

长沙理工大学数学与统计学院,长沙,410114

出版日期:2017-03-30 发布日期:2020-09-24
基金资助:
国家自然科学基金资助项目(11371072)

Solving a Class of Matrix Equations by Sparse Approximate Inverse Preconditioning

Deng Miao， Zhou Fuzhao

School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China

Online:2017-03-30 Published:2020-09-24

摘要/Abstract

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.

关键词: 矩阵方程, 正交投影迭代法, 预条件, 稀疏近似逆

Abstract: In this paper a F-norm minimization based sparse approximate inverse preconditioning for solving a class of matrix equations is given.Firstly,the effective preconditioner is find by the F-norm minimization based sparse approximate inverse preconditioning technique,then a algorithm is given by applying the obtained preconditioner 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.

Key words:

Matrix equation, Orthogonal projection iterative algorithm , Preconditioning, Sparse approximate inverse

邓淼, 周富照. 稀疏近似逆预处理求解一类矩阵方程[J]. 数学理论与应用, 2017, 37(1): 38-43.

Deng Miao, Zhou Fuzhao. Solving a Class of Matrix Equations by Sparse Approximate Inverse Preconditioning[J]. Mathematical Theory and Applications, 2017, 37(1): 38-43.

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