Dykstra's algorithm and applications to inverse best approximations - Dizon, Neil Kristofer V. (Institute of Mathematics, College of Science, University of the Philippines Diliman, 2016)
The method of alternating projections (MAP) is a theoretically powerful method for finding best approximations from the intersection of a finite number of closed convex sets. In this paper, we present a survey of important results on the methods of alternating projections with emphasis on the Dykstra's algorithm.We apply the Dykstra's projection scheme coupled with a robust stopping rule in solving inverse best approximation problems numerically. Among others, a simple signal recovery problem is provided as an example. Moreover, given an operator equation involving a metric projection onto the level sets of convex and gateaux differentiable function, we obtain an estimate on how the norm of approximate solutions blows u as the error of approximation converges to zero.