一类绝对值方程的修正SOR类迭代法

A Modified SOR-like Iteration Method for the Absolute Value Equations

在本文中,针对一类NP-难问题,即绝对值方程(AVEs),我们提出了修正的逐次超松弛(MSOR)类方法.当系统矩阵非奇异且其奇异值都超过1时,我们讨论了该迭代法的全局收敛性.此外,我们给出了松弛因子最优值的一个估计表达式.最后,数值结果表明所提出的迭代方法是有效性.

In this paper, a modified successive over relaxation （MSOR） -like iteration method is suggested and analyzed for solving the NP- hard absolute value equations （AVEs）. When the system matrix is nonsingular and all of its singular values exceed 1, we discuss the global convergence of the proposed iteration method. Furthermore, we also give an estimation of the optimal value of the relaxation factor. Comparative numerical results are presented to substantiate the efficacy of the proposed iteration method.