2012/06/15 by Heinz H. Bauschke, Bauschke, Heinz H., Joshua Sarada +3
Mathematics · #15B51 #26E60 #47H10 (Primary) 39A06 #47J25 #49J53 (Secondary) #65H04 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #math.CA #math.FA #math.OC #msc:15B51 #msc:26E60 #msc:39A06 #msc:47H10 #msc:47J25 #msc:49J53 #msc:65H04
paper · pdf · doi:10.48550/arxiv.1206.3610
arxiv created 2012/06/15 · arxiv updated 2012/06/19
We show that the moving arithmetic average is closely connected to a Gauss-Seidel type fixed point method studied by Bauschke, Wang and Wylie, and which was observed to converge only numerically. Our analysis establishes a rigorous proof of convergence of their algorithm in a special case; moreover, limit is explicitly identified. Moving averages in Banach spaces and Kolmogorov means are also studied. Furthermore, we consider moving proximal averages and epi-averages of convex functions.