论文标题
异步理查森迭代
Asynchronous Richardson iterations
论文作者
论文摘要
我们考虑第一和二阶Richardson方法的异步版本，用于求解方程的线性系统。这些方法取决于选择值的参数。我们探索可以证明可以证明具有异步方法收敛的参数值。这是异步二阶方法的第一个这样的分析。我们发现，对于一阶方法，同步案例的最佳参数值还提供了异步收敛的方法。对于第二阶方法，我们可以证明异步收敛的参数范围不包含同步迭代的最佳参数值。但是，在实践中，尽管结果结果，但异步的二阶迭代仍可以使用最佳参数值或接近最佳的参数值收敛。我们通过异步方法的多线程并行实现探索这种行为。
We consider asynchronous versions of the first and second order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chosen a priori. We explore the parameter values that can be proven to give convergence of the asynchronous methods. This is the first such analysis for asynchronous second order methods. We find that for the first order method, the optimal parameter value for the synchronous case also gives an asynchronously convergent method. For the second order method, the parameter ranges for which we can prove asynchronous convergence do not contain the optimal parameter values for the synchronous iteration. In practice, however, the asynchronous second order iterations may still converge using the optimal parameter values, or parameter values close to the optimal ones, despite this result. We explore this behavior with a multithreaded parallel implementation of the asynchronous methods.
