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On moving averages
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
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