In this paper, we tackled the convergence detection problem arisen from the absence of synchronization during asynchronous iterative computation. We showed that, when one arbitrarily takes the local components of a global solution vector, an upper bound can be established on the difference between a residual error evaluated from this global vector and the inconsistent residual error evaluated without synchronizing the involved computing processes. This allows for accurate termination of asynchronous iterations without implementing any particular detection protocol. Termination delay has be handled too for not slowing down the overall asynchronous solver, by appropriately setting the convergence threshold criterion. We therefore ensured effectiveness while reaching better efficiency in terms of overall execution time of the solver, in comparison with the current most efficient exact snapshot-based approach.

在本文中，我们解决了由于异步迭代计算过程中缺少同步而引起的收敛检测问题。我们证明了，当一个人任意取全局解向量的局部分量时，可以在不同步所涉及的计算过程的情况下，确定从该全局向量评估的残差误差与评估的不一致残差之间的差异的上限。这允许异步迭代的准确终止，而无需实现任何特定的检测协议。通过适当设置收敛阈值标准，还可以处理终止延迟，以免降低整体异步求解器的速度。因此，我们在确保效率的同时，还提高了求解器的整体执行时间，