A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf H$-matrices. The computational model can be thought of as a two-stage alternating iterative method, which well suits to the well-known Hermitian and skew-Hermitian splitting (HSS) approach, with the particularity here of considering only one inner iteration. Experimental parallel performance comparison is conducted between the generalized minimal residual (GMRES) algorithm, the standard HSS and our asynchronous variant, on both real and complex non-Hermitian linear systems respectively arising from convection-diffusion and structural dynamics problems. A significant gain on execution time is observed in both cases.

翻译：设计了一种通用的异步交替迭代模型，并在经典谱半径界条件下以及针对$\mathsf H$-矩阵的一类经典矩阵分裂中，从理论上保证了其收敛性。该计算模型可视为一种两阶段交替迭代方法，非常适用于著名的Hermitian与skew-Hermitian分裂（HSS）框架，其特殊之处在于仅考虑一次内迭代。针对分别来自对流-扩散问题和结构动力学问题的实非Hermitian与复非Hermitian线性系统，进行了广义最小残差（GMRES）算法、标准HSS方法及本文异步变体之间的并行性能对比实验。在两种情形下均观察到执行时间的显著减少。