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

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.