论文标题
关于Dykstra的算法：有限收敛，失速和交替预测的方法
On Dykstra's algorithm: finite convergence, stalling, and the method of alternating projections
论文作者
论文摘要
Dykstra的算法是在Hilbert Space中发现投影到两个封闭凸子集交点的流行方法。在本文中，我们为Dykstra的算法提供了足够的条件，可以在有限的许多步骤中快速收敛。我们还分析了Dykstra算法应用于线和正方形的行为。该案例研究揭示了与交替预测方法的明显相似之处。此外，我们表明，Dykstra的算法可能任意停滞了很长时间。最后，我们提出了一些开放问题。
A popular method for finding the projection onto the intersection of two closed convex subsets in Hilbert space is Dykstra's algorithm. In this paper, we provide sufficient conditions for Dykstra's algorithm to converge rapidly, in finitely many steps. We also analyze the behaviour of Dykstra's algorithm applied to a line and a square. This case study reveals stark similarities to the method of alternating projections. Moreover, we show that Dykstra's algorithm may stall for an arbitrarily long time. Finally, we present some open problems.
