The generalized Stein-Rosenberg type theorem is established for the parallel decomposition-type accelerated overrelaxation method (PDAOR-method) for solving the large scale block systems of linear equations. This thereby affords reliable criterions for judging the convergence and divergence, as well as the convergence rate and divergence rate, of this PDAOR-method.
For a class of ideal models of parallel computers, we define some measuring parameters such as the speed-up, the efficiency, the redundancy of a linear and nonlinear parallel iteration method in both average and asymptotic senses, as well as the utilization ratio of the parallel computer. These parameters are reasonable and convenient for the theoretical studies of the parallel iteration methods.
提出了求解广义Lyapunov方程的HSS(Hermitian and skew-Hermitian splitting)迭代法,分析了该方法的收敛性,给出了收敛因子的上界.为了降低HSS迭代法的计算量,提出了求解广义Lyapunov方程的非精确HSS迭代法,并分析其收敛性.数值结果表明,求解广义Lyapunov方程的HSS迭代法及非精确HSS迭代法是有效的.
