On moving averages
Functional Analysis
2012-06-19 v1 Classical Analysis and ODEs
Optimization and Control
Abstract
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.
Cite
@article{arxiv.1206.3610,
title = {On moving averages},
author = {Heinz H. Bauschke and Joshua Sarada and Xianfu Wang},
journal= {arXiv preprint arXiv:1206.3610},
year = {2012}
}