论文标题
局部适当的环状方法的有限收敛
Finite convergence of locally proper circumcentered methods
论文作者
论文摘要
考虑到解决最佳近似问题的周围等轴测方法的出色性能，在这项工作中，我们进一步研究了局部适当的圆周映射和周围的方法。列出和研究了各种局部适当的围栏映射的例子。在最近的论文中，受Behling，Bello-Cruz和Santos对周围反射方法的一些结果的启发，我们为一个循环等轴测方法的一步收敛提供了足够的条件，以找到与相关异透镜固定点集的交叉点，以找到最佳的近似值。此外，我们详细阐述了与超平面和半空间相关的反射器引起的周围反射方法的性能，以在超平面和半空间的相交中找到最佳的近似点（或一个点）。
In view of the great performance of circumcentered isometry methods for solving the best approximation problem, in this work we further investigate the locally proper circumcenter mapping and circumcentered method. Various examples of locally proper circumcenter mapping are presented and studied. Inspired by some results on circumcentered-reflection method by Behling, Bello-Cruz, and Santos in their recent papers, we provide sufficient conditions for one step convergence of circumcentered isometry methods for finding the best approximation point onto the intersection of fixed point sets of related isometries. In addition, we elaborate the performance of circumcentered reflection methods induced by reflectors associated with hyperplanes and halfspaces for finding the best approximation point onto (or a point in) the intersection of hyperplanes and halfspaces.
