求解具有多个右端项线性方程组的HBFGl-GMRES方法

Heavy Ball Flexible Global GMRES Method for Linear Systems with Multiple Right-Hand Sides

重启灵活预处理总体广义极小残差(FGl-GMRES)方法是求解具有多个右端项线性方程组的经典迭代方法之一。然而重启会丢失旧循环Krylov子空间产生的信息,因此重启Gl-GMRES方法和FGl-GMRES方法在求解一些具有多个右端项线性方程组时常常出现收敛速度慢或不收敛的情形。为了加快重启Gl-GMRES方法和FGl-GMRES方法的收敛速度,使用Heavy ball技术,提出了求解具有多个右端项线性方程组的Heavy ball Gl-GMRES方法(HBGl-GMRES)和Heavy ball FGl-GMRES方法(HBFGl-GMRES)。最后,数值实验结果验证了新方法的有效性。

The restart flexible preconditioned global generalized minimal residual(FGl-GMRES)method is one of the classical iterative methods for solving linear systems with multiple right-hand sides.However,due to ignoring the history information in the previous cycles,Gl-GMRES and FGl-GMRES often return slow convergence rate or cannot converge for solving some practical linear systems with multiple right-hand sides.In this paper,in order to accelerate the convergence rate of Gl-GMRES and FGl-GMRES,we propose the heavy ball Gl-GMRES(HBGl-GMRES)method and flexible Gl-GMRES(HBFGl-GMRES)method based on heavy ball technique.Finally,numerical results demonstrate the effectiveness of our new methods.