  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.

Numerical Analysis;Distributed, Parallel, and Cluster Computing;Numerical Analysis