仿射子空间的Gearhart-Koshy加速
Gearhart-Koshy Acceleration for Affine Subspaces
摘要：
循环投影法是在多个仿射子空间的交集中寻找最近点的一种方法。为了加速收敛，Gearhart和Koshy提出了一种修改，在每次迭代中，基于最小化到解的距离执行精确的线搜索。当子空间是线性的时，可以利用零向量的可行性使该过程显式化。这项工作研究了一种替代方法，它不依赖于这一事实，从而提供了一个有效的实施仿射设置。
英文摘要：
The method of cyclic projections finds nearest points in the intersection of finitely many affine subspaces. To accelerate convergence, Gearhart and Koshy proposed a modification which, in each iteration, performs an exact line search based on minimising the distance to the solution. When the subspaces are linear, the procedure can be made explicit using feasibility of the zero vector. This work studies an alternative approach which does not rely on this fact, thus providing an efficient implementation in the affine setting.
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