论文标题
仿射子空间的Gearhart-Koshy加速度
Gearhart-Koshy Acceleration for Affine Subspaces
论文作者
论文摘要
循环投影方法在有限的许多仿射子空间的交集中找到了最近的点。为了加速收敛，Gearhart和Koshy提出了一种修改，在每次迭代中，它都会基于最小化溶液的距离进行精确的线路搜索。当子空间是线性的时，可以使用零向量的可行性明确地进行过程。这项工作研究了一种不依赖这一事实的替代方法，因此在仿射环境中提供了有效的实施。
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.
