论文标题
一种新的迭代方法，用于求解一类两乘两块块复合线性系统
A new iterative method for solving a class of two-by-two block complex linear systems
论文作者
论文摘要
我们提出了一种固定的迭代方法，即通过使用分布式最佳控制问题的有限元离散化与时间周期性抛物线方程的有限元隔离化，以解决对称的对称正定确定和缩放对称阳性半脱位（ASS）。给出了迭代方法光谱半径的上限，该频谱半径始终小于1。因此，保证了屁股迭代方法的收敛性。诱导的屁股预处理用于加速GMRES方法的收敛速度以求解系统。提出了数值结果，以证明屁股迭代方法和屁股预处理的有效性。
We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization of a distributed optimal control problem together with time-periodic parabolic equations. An upper bound for the spectral radius of the iteration method is given which is always less than 1. So convergence of the ASSS iteration method is guaranteed. The induced ASSS preconditioner is applied to accelerate the convergence speed of the GMRES method for solving the system. Numerical results are presented to demonstrate the effectiveness of both the ASSS iteration method and the ASSS preconditioner.
