论文标题
在角度，预测和迭代
On angles, projections and iterations
论文作者
论文摘要
我们研究了线性子空间的几何形状与线性投影交替投影方法的收敛性之间的连接。本文的目的是双重的：在第一部分中，我们表明，即使在欧几里得空间中，交替方法的收敛也不能由所涉及的子空间之间的主要角度确定。在第二部分中，我们研究了两个线性投影之间的Oppenheim角的性质。我们特别讨论了在这种情况下的存在和“一致性预测”的独特性问题。
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean spaces the convergence of the alternating method is not determined by the principal angles between the subspaces involved. In the second part, we investigate the properties of the Oppenheim angle between two linear projections. We discuss, in particular, the question of existence and uniqueness of "consistency projections" in this context.
