Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Heinz H. Bauschke

Dept. of Mathematics, University of British Columbia, Kelowna, B.C. V1V 1V7, Canada

heinz.bauschke@ubc.ca

Xianfu Wang

Dept. of Mathematics, University of British Columbia, Kelowna, B.C. V1V 1V7, Canada

shawn.wang@ubc.ca

Keywords

  • Arithmetic mean
  • difference equation
  • epi-average
  • Kolmogorov mean
  • linear recurrence relation
  • means
  • moving average
  • proximal average
  • stochastic matrix

Mathematics Subject Classification

15B51, 26E60, 47H10; 39A06, 65H04, 47J25, 49J53

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Suggested citation

H. H. Bauschke, J. Sarada, X. Wang. “On Moving Averages.” Journal of Convex Analysis 21 (2014), No. 1, 219–235. https://doi.org/10.68381/jca21012

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.