Geodesic
On Moving Averages
Journal of convex analysis, Tome 21 (2014) no. 1, pp. 219-235

Voir la notice de l'article provenant de la source Heldermann Verlag

We show that the moving arithmetic average is closely connected to a Gauss-Seidel type fixed point method studied by H. H. Bauschke, X. Wang and C. J. S. Wylie [Fixed points of averages of resolvents: geometry and algorithms, SIAM J. Optimization 22 (2012) 24--40] and which was observed to converge only numerically. Our analysis establishes a rigorous proof of convergence of their algorithm in a special case; moreover, the 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.
Classification : 15B51, 26E60, 47H10, 39A06, 65H04, 47J25, 49J53
Mots-clés : Arithmetic mean, difference equation, epi-average, Kolmogorov mean, linear recurrence relation, means, moving average, proximal average, stochastic matrix 
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H. H. Bauschke; J. Sarada; X. Wang. On Moving Averages. Journal of convex analysis, Tome 21 (2014) no. 1, pp. 219-235. http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a11/